Difference between revisions of "Calorimeter"

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''This article is about heat measuring devices. For particle detectors, see'' <span class="plainlinks">[http://en.wikipedia.org/wiki/Calorimeter_(particle_physics)?title=Calorimeter Calorimeter (particle physics)]</span>
{{About|heat measuring devices|particle detectors|Calorimeter (particle physics)}}


[[Image:Ice-calorimeter.jpg|150px|right|thumb|The world’s first '''ice-calorimeter''', used in the winter of 1782-83, by <span class="plainlinks">[http://en.wikipedia.org/wiki/Antoine_Lavoisier?title=AntoineLavoisier Antoine Lavoisier]</span>
[[Image:Ice-calorimeter.jpg|150px|right|thumb|The world’s first '''ice-calorimeter''', used in the winter of 1782-83, by Antoine Lavoisier and Pierre-Simon Laplace, to determine the heat evolved in various chemical changes; calculations which were based on Joseph Black's prior discovery of latent heat.  These experiments mark the foundation of [[thermochemistry]].]]  
and <span class="plainlinks">[http://en.wikipedia.org/wiki/Pierre-Simon_Laplace?title=PierreSimonLaplace Pierre-Simon Laplace]</span>
A '''calorimeter''' (from Latin ''calor'', meaning heat) is an object used for calorimetry, the process of measuring the heat of chemical reactions or physical changes as well as heat capacity. More specifically, a calorimeter handles the [[enthalpy]] changes of chemical reactions by thermally isolating the reaction system from its surroundings.<ref name="AdvChemCalo">{{cite book |url=http://books.google.com/books?id=qciCdSFpFPkC&pg=PA149 |title=Advanced Chemistry |author=Clugston, Michael J.; Flemming, Rosalind |publisher=Oxford University Press |year=2000 |page=148 |isbn=0199146330}}</ref> A simple calorimeter just consists of a thermometer attached to a metal container full of water suspended above a combustion chamber and is sometimes referred to as a "coffee cup" calorimeter, whereas more sophisticated forms like "flame" and "bomb" calorimeters involve combustion of the substance in a burner or pressurized vessel.
, to determine the <span class="plainlinks">[http://en.wikipedia.org/wiki/Heat?title=heat heat]</span> evolved in various <span class="plainlinks">[http://en.wikipedia.org/wiki/Chemical_change?title=ChemicalChange chemical change(s)]</span>
; calculations which were based on <span class="plainlinks">[http://en.wikipedia.org/wiki/Joseph_Black?title=JosephBlack Joseph Black]</span> ’s prior discovery of <span class="plainlinks">[http://en.wikipedia.org/wiki/Latent_heat?title=LatentHeat latent heat]</span>.  These experiments mark the foundation of <span class="plainlinks">[http://en.wikipedia.org/wiki/Thermochemistry?title=Thermochemistry thermochemistry]</span> thermochemistry.]]  
A '''calorimeter''' (from <span class="plainlinks">[http://en.wikipedia.org/wiki/Latin?title=Latin Latin]</span> ''calor'', meaning <span class="plainlinks">[http://en.wikipedia.org/wiki/Heat?title=heat heat]</span>) is a device used for  
<span class="plainlinks">[http://en.wikipedia.org/wiki/Calorimetry?title=Calorimetry calorimetry]</span>, the  
<span class="plainlinks">[http://en.wikipedia.org/wiki/Science?title=Science science]</span> of measuring the heat of  
<span class="plainlinks">[http://en.wikipedia.org/wiki/Chemical_reaction?title=ChemicalReaction chemical reaction]</span>s or
<span class="plainlinks">[http://en.wikipedia.org/wiki/Physical_change?title=PhysicalChange physical change]</span>s as well as <span class="plainlinks">[http://fr.wikipedia.org/w/index.php?title=HeatCapacity heat capacity]</span>. Differential scanning calorimeters, isothermal microcalorimeters, titration calorimeters and accelerated rate calorimeters are among the most common types. A simple calorimeter just consists of a thermometer attached to a metal container full of water suspended above a combustion chamber.


To find the  
To find the enthalpy change per mole of a substance A in a reaction between two substances A and B, the substances are added to a calorimeter and the initial and final temperatures (before the reaction started and after it has finished) are noted. Multiplying the temperature change by the mass and specific heat capacities of the substances gives a value for the energy given off or absorbed during the reaction. Dividing the energy change by how many moles of A were present gives its enthalpy change of reaction. This method is used primarily in academic teaching as it describes the theory of calorimetry.<ref name="AdvChemCalo" /> It does not account for the heat loss through the container or the heat capacity of the thermometer and container itself. In addition, the object placed inside the calorimeter shows that the objects transferred their heat to the calorimeter and into the liquid, and the heat absorbed by the calorimeter and the liquid is equal to the heat given off by the metals.<ref name="ChemPrinCalo">{{cite book |url=http://books.google.com/books?id=2OxrDtDaSqIC&pg=PA378 |title=Chemical Principles |author=Zumdahl, Steven S. |publisher=Cengage Learning |year=2009 |page=378–87 |isbn=061894690X}}</ref>
<span class="plainlinks">[http://en.wikipedia.org/wiki/Enthalpy?title=Enthalpy enthalpy]</span> change per  
 
<span class="plainlinks">[http://en.wikipedia.org/wiki/Mole_(unit)?title=Mole mole]</span> of a substance A in a reaction between two substances A and B, the substances are added to a calorimeter and the initial and final  
==History==
<span class="plainlinks">[http://en.wikipedia.org/wiki/Temperature?title=Temperature temperature]</span>s (before the reaction started and after it has finished) are noted. Multiplying the temperature change by the mass and  
In 1780, Antoine Lavoisier used a Guinea pig in his experiments with the calorimeter, a device used to measure heat production. The heat from the guinea pig's respiration melted snow surrounding the calorimeter, showing that respiratory gas exchange is a combustion, similar to a candle burning.<ref name="CalorieJournalNutr">{{cite journal |url=http://www.ajcn.org/cgi/content/full/79/5/899S |journal=American Journal of Clinical Nutrition |volume=79 |issue=5 |page=899S–906S |year=2004 |author=Buchholz, Andrea C; Schoeller, Dale A. |title=Is a Calorie a Calorie? |PMID=15113737 |accessdate=01 March 2013}}</ref>
<span class="plainlinks">[http://en.wikipedia.org/wiki/Specific_heat_capacity?title=SpeHeatCapacity specific heat capacities]</span>
of the substances gives a value for the  
<span class="plainlinks">[http://en.wikipedia.org/wiki/Energy?title=Energy energy]</span> given off or absorbed during the reaction. Dividing the energy change by how many moles of A were present gives its enthalpy change of reaction. This method is used primarily in academic teaching as it describes the theory of calorimetry. It does not account for the heat loss through the container or the heat capacity of the thermometer and container itself. In addition, the object placed inside the calorimeter show that the objects transferred their heat to the calorimeter and into the liquid, and the heat absorbed by the calorimeter and the liquid is equal to the heat given off by the metals.


==Adiabatic calorimeters==
==Adiabatic calorimeters==
An  
An adiabatic calorimeter is a calorimeter used to examine a runaway reaction. Since the calorimeter runs in an adiabatic environment, any heat generated by the material sample under test causes the sample to increase in temperature, thus fueling the reaction.
<span class="plainlinks">[http://en.wikipedia.org/wiki/Adiabatic_process?title=Adiabatic adiabatic]</span> calorimeter is a calorimeter used to examine a runaway reaction. Since the calorimeter runs in an adiabatic environment, any heat generated by the material sample under test causes the sample to increase in temperature, thus fuelling the reaction.<br>
 
No adiabatic calorimeter is truly adiabatic - some heat will be lost by the sample to the sample holder. Examples of adiabatic calorimeters are:-
No adiabatic calorimeter is adiabatic some heat will be lost by the sample to the sample holder. A mathematical correction factor, known as the phi-factor, can be used to adjust the calorimetric result to account for these heat losses. The phi-factor is the ratio of the thermal mass of the sample and sample holder to the thermal mass of the sample alone.<ref name="SHMMM83">{{cite book |url=http://books.google.com/books?id=8lANaR-Pqi4C&pg=PA410 |title=Springer Handbook of Materials Measurement Methods |editor=Czichos, Horst ; Saito, Tetsuya; Smith, Leslie R. |publisher=Springer |year=2006 |page=410–414 |isbn=3540303006 |accessdate=08 May 2013}}</ref>
* THT EV-Accelerating Rate Calorimeter<ref>[http://en.wikipedia.org/wiki/Calorimeter#cite_note-0]</ref>
* HEL Phi-Tec<ref>[http://en.wikipedia.org/wiki/Calorimeter#cite_note-1]</ref>
* A simple <span class="plainlinks">[http://en.wikipedia.org/wiki/Dewar_flask?title=DewarFlask Dewar flask]</span>
* Systag FlexyTSC<ref>[http://en.wikipedia.org/wiki/Calorimeter#cite_note-2 Systag FlexyTSC]</ref> a successor of their SIKAREX unit - the electronics of which could be used to apply a feedback system to heat the sample holder to give a result closer to true adiabaticy, however as the sample holder is an open ended glass tube, one soon loses the sample as a great deal of smoke.


==Reaction calorimeters==
==Reaction calorimeters==


''Main article:''<span class="plainlinks">[http://en.wikipedia.org/wiki/Reaction_calorimeters?title=ReactionCalorimeters Reaction calorimeters]</span>.
A reaction calorimeter is a calorimeter in which a chemical reaction is initiated within a closed insulated container. Reaction heats are measured and the total heat is obtained by integrating heat flow versus time. This is the standard used in industry to measure heats since industrial processes are engineered to run at constant temperatures. Reaction calorimetry can also be used to determine maximum heat release rate for chemical process engineering and for tracking the global kinetics of reactions.<ref name="IORCalor">{{cite book |url=http://books.google.com/books?id=NgV9yqD-sOYC&pg=PA200 |title=The Investigation of Organic Reactions and Their Mechanisms |editor=Maskill, Howard |publisher=John Wiley & Sons |year=2008 |page=200–202 |isbn=0470994169 |accessdate=08 May 2013}}</ref> There are four main methods for measuring the heat in reaction calorimeter:
 
 
A reaction calorimeter is a calorimeter in which a  
<span class="plainlinks">[http://en.wikipedia.org/wiki/Chemical_reaction?title=ChemicalReaction chemical reaction]</span> is initiated within a closed insulated container. Reaction heats are measured and the total heat is obtained by integrating heatflow versus time. This is the standard used in industry to measure heats since industrial processes are engineered to run at constant temperatures. Reaction calorimetry can also be used to determine maximum heat release rate for chemical process engineering and for tracking the global kinetics of reactions. There are four main methods for measuring the heat in reaction calorimeter:


===Heat flow calorimetry===
===Heat flow calorimetry===


The cooling/heating jacket controls either the temperature of the process or the temperature of the jacket. Heat is measured by monitoring the temperature difference between heat transfer fluid and the process fluid. In addition fill volumes (i.e. wetted area), specific heat, heat transfer coefficient have to be determined to arrive at a correct value.  It is possible with this type of calorimeter to do reactions at reflux, although the accuracy is not as good.
The cooling/heating jacket controls either the temperature of the process or the temperature of the jacket. Heat is measured by monitoring the temperature difference between heat transfer fluid and the process fluid. In addition fill volumes (i.e. wetted area), specific heat, heat transfer coefficient have to be determined to arrive at a correct value.  It is possible with this type of calorimeter to do reactions at reflux, although the accuracy is not as good.<ref name="IORCalor" />


===Heat balance calorimetry===
===Heat balance calorimeter===


The cooling/heating jacket controls the temperature of the process. Heat is measured by monitoring the heat gained or lost by the heat transfer fluid.
The cooling/heating jacket controls the temperature of the process. Heat is measured by monitoring the heat gained or lost by the heat transfer fluid.<ref name="IORCalor" />


===Power compensation===
===Power compensation===
Power compensation uses a heater placed within the vessel to maintain a constant temperature. The energy supplied to this heater can be varied as reactions require and the calorimetry signal is purely derived from this electrical power.
Power compensation uses a heater placed within the vessel to maintain a constant temperature. The energy supplied to this heater can be varied as reactions require and the calorimetry signal is purely derived from this electrical power.<ref name="IORCalor" />


===Constant flux===
===Constant flux===
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[[File:Bombenkalorimeter mit bombe.jpg|thumb|Bomb calorimeter]]
[[File:Bombenkalorimeter mit bombe.jpg|thumb|Bomb calorimeter]]
[[File:Bomb Calorimeter.png|thumb|Bomb calorimeter]]


A bomb calorimeter is a type of constant-volume calorimeter used in measuring the heat of combustion of a particular reaction. Bomb calorimeters have to withstand the large pressure within the calorimeter as the reaction is being measured. Electrical energy is used to ignite the fuel; as the fuel is burning, it will heat up the surrounding air, which expands and escapes through a tube that leads the air out of the calorimeter. When the air is escaping through the copper tube it will also heat up the water outside the tube. The temperature of the water allows for calculating calorie content of the fuel.
A bomb calorimeter is a type of constant-volume calorimeter used in measuring the heat of combustion of a particular reaction. Bomb calorimeters have to withstand the large pressure within the calorimeter as the reaction is being measured. Electrical energy is used to ignite the fuel; as the fuel is burning, it will heat up the surrounding air, which expands and escapes through a tube that leads the air out of the calorimeter. When the air is escaping through the copper tube it will also heat up the water outside the tube. The temperature of the water allows for calculating calorie content of the fuel.<ref name="SHMMM83" /><ref name="AdvChemCalo" />


In more recent calorimeter designs, the whole bomb, pressurized with excess pure oxygen (typically at 30atm) and containing a known mass of sample (typically 1-1.5 g) and a small fixed amount of water (to absorb produced acid gases), is submerged under a known volume of water (ca.&nbsp;2000 ml) before the charge is (again electrically) ignited. The bomb, with sample and oxygen, form a closed system - no air escapes during the reaction. The energy released by the combustion raises the temperature of the steel bomb, its contents, and the surrounding water jacket. The temperature change in the water is then accurately measured. This temperature rise, along with a bomb factor (which is dependent on the heat capacity of the metal bomb parts) is used to calculate the energy given out by the sample burn. A small correction is made to account for the electrical energy input, the burning fuse, and acid production (by titration of the residual liquid). After the temperature rise has been measured, the excess pressure in the bomb is released.
In more recent calorimeter designs, the whole bomb, pressurized with excess pure oxygen (typically at 30atm) and containing a weighed mass of a sample (typically 1-1.5 g) and a small fixed amount of water (to saturate the internal atmosphere, thus ensuring that all water produced is liquid, and removing the need to include enthalpy of vaporization in calculations), is submerged under a known volume of water (ca.&nbsp;2000 ml) before the charge is electrically ignited. The bomb, with the known mass of the sample and oxygen, form a closed system - no gases escape during the reaction. The weighted reactant put inside the steel container is then ignited. Energy is released by the combustion and heat flow from this crosses the stainless steel wall, thus raising the temperature of the steel bomb, its contents, and the surrounding water jacket. The temperature change in the water is then accurately measured with a thermometer. This reading, along with a bomb factor (which is dependent on the heat capacity of the metal bomb parts), is used to calculate the energy given out by the sample burn. A small correction is made to account for the electrical energy input, the burning fuse, and acid production (by titration of the residual liquid). After the temperature rise has been measured, the excess pressure in the bomb is released.


Basically, a bomb calorimeter consists of a small cup to contain the sample, oxygen, a stainless steel bomb, water, a stirrer, a thermometer, the dewar (to prevent heat flow from the calorimeter to the surroundings) and ignition circuit connected to the bomb.  
Basically, a bomb calorimeter consists of a small cup to contain the sample, oxygen, a stainless steel bomb, water, a stirrer, a thermometer, the dewar or insulating container (to prevent heat flow from the calorimeter to the surroundings) and ignition circuit connected to the bomb. By using stainless steel for the bomb, the reaction will occur with no volume change observed.  


Since there is no heat exchange between the calorimeter and surroundings → Q = 0 (adiabatic) ; no work performed → W = 0
Since there is no heat exchange between the calorimeter and surroundings → Q = 0 (adiabatic) ; no work performed → W = 0
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A length of Nickel fuse wire (~10&nbsp;cm) is weighed both before and after the combustion process. Mass of fuse wire burned Δm = m(before) - m(after)
A length of Nickel fuse wire (~10&nbsp;cm) is weighed both before and after the combustion process. Mass of fuse wire burned Δm = m(before) - m(after)


The combustion of sample (benzoic acid) inside the bomb ΔH<sub>c</sub> = ΔH<sub>c</sub> (benzoic acid) x m (benzoic aicd) + ΔH<sub>c</sub> (Ni fuse wire) x Δm (Ni fuse wire)
The combustion of sample (benzoic acid) inside the bomb ΔH<sub>c</sub> = ΔH<sub>c</sub> (benzoic acid) x m (benzoic acid) + ΔH<sub>c</sub> (Ni fuse wire) x Δm (Ni fuse wire)


ΔH<sub>c</sub> = C<sub>v</sub>. ΔT → C<sub>v</sub> = ΔH<sub>c</sub>/ΔT
ΔH<sub>c</sub> = C<sub>v</sub>. ΔT → C<sub>v</sub> = ΔH<sub>c</sub>/ΔT


Once C<sub>v</sub> value of the bomb is determined, the bomb is ready to use to calculate heat of combustion of any compounds by ΔH<sub>c</sub> = C<sub>v</sub>. ΔT
Once C<sub>v</sub> value of the bomb is determined, the bomb is ready to use to calculate heat of combustion of any compounds by ΔH<sub>c</sub> = C<sub>v</sub>. ΔT<ref name="Polik">{{cite web |url=http://www.chem.hope.edu/~polik/Chem345-1997/calorimetry/bombcalorimetry1.html |title=Bomb Calorimetry |author=Polik, W. |publisher=Hope College Chemistry Department |date=1997 |accessdate=01 March 2013}}</ref>
 
==Calvet-type calorimeters==


<ref>Polik, W. (1997). Bomb Calorimetery. Retrieved from http://www.chem. hope. edu/ ~polik/Chem345-1997/calorimetry/bombcalorimetry1.html</ref>
The detection is based on a three-dimensional fluxmeter sensor. The fluxmeter element consists of a ring of several thermocouples in series. The corresponding thermopile of high thermal conductivity surrounds the experimental space within the calorimetric block. The radial arrangement of the thermopiles guarantees an almost complete integration of the heat. This is verified by the calculation of the efficiency ratio that indicates that an average value of 94% +/- 1% of heat is transmitted through the sensor on the full range of temperature of the Calvet-type calorimeter. In this setup, the sensitivity of the calorimeter is not affected by the crucible, the type of purge gas, or the flow rate. The main advantage of the setup is the increase of the experimental vessel's size and consequently the size of the sample, without affecting the accuracy of the calorimetric measurement.<ref name="HTACCalor">{{cite book |url=http://books.google.com/books?id=33_3DBLGzMYC&pg=PR619 |title=Handbook of Thermal Analysis and Calorimetry: Principles and Practice |editor=Brown, Michael E. |publisher=Elsevier |year=1998 |page=619–629 |isbn=0080539599 |accessdate=08 May 2013}}</ref>
<ref>Bozzelli, J. (2010). Heat of Combustion via Calorimetry: Detailed Procedures. Chem 339-Physical Chemistry Lab for Chemical Engineers –Lab Manual.</ref>


==Calvet-type calorimeters==
The calibration of the calorimetric detectors is a key parameter and has to be performed very carefully. For Calvet-type calorimeters, a specific calibration, so called Joule effect or electrical calibration, has been developed to overcome all the problems encountered by a calibration done with standard materials.
The detection is based on a three-dimensional fluxmeter sensor. The fluxmeter element consists of a ring of several thermocouples in series. The corresponding thermopile of high thermal conductivity surrounds the experimental space within the calorimetric block. The radial arrangement of the thermopiles guarantees an almost complete integration of the heat. This is verified by the calculation of the efficiency ratio that indicates that an average value of 94 % +/- 1 % of heat is transmitted through the sensor on the full range of temperature of the Calvet-type calorimeter. In this setup, the sensitivity of the calorimeter is not affected by the crucible, the type of purgegas, or the flow rate. The main advantage of the setup is the increase of the experimental vessel's size and consequently the size of the sample, without affecting the accuracy of the calorimetric measurement.


The calibration of the calorimetric detectors is a key parameter and has to be performed very carefully. For Calvet-type calorimeters, a specific calibration, so called
<span class="plainlinks">[http://en.wikipedia.org/wiki/Joule_effect?title=JouleEffect Joule effect]</span> or electrical calibration, has been developed to overcome all the problems encountered by a calibration done with standard materials.
The main advantages of this type of calibration are as follows:
The main advantages of this type of calibration are as follows:
*It is an absolute calibration.
*It is an absolute calibration.
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*It is a very accurate calibration.
*It is a very accurate calibration.


An example of Calvet-type calorimeter is the C80 Calorimeter (reaction, isothermal and scanning calorimeter).<ref name="Calvet-type calorimeter">[http://www.setaram.com/C80.htm C80 Calorimeter from Setaram Instrumentation]</ref>
An example of Calvet-type calorimeter is the C80 Calorimeter (reaction, isothermal and scanning calorimeter).<ref name="Calvet-type calorimeter">{{cite web |url=http://www.setaram.com/C80.htm C80 |title=Calorimetry C-80 |publisher=Setaram Instrumentation |accessdate=01 March 2013}}</ref>


==Constant-pressure calorimeter==
==Constant-pressure calorimeter==


A '''constant-pressure calorimeter''' measures the change in  
A '''constant-pressure calorimeter''' measures the change in enthalpy of a reaction occurring in solution during which the atmospheric pressure remains constant.
<span class="plainlinks">[http://en.wikipedia.org/wiki/Enthalpy?title=Enthalpy enthalpy]</span> of a reaction occurring in  
<span class="plainlinks">[http://en.wikipedia.org/wiki/Solution?title=Solution solution]</span> during which the  
<span class="plainlinks">[http://en.wikipedia.org/wiki/Atmospheric_pressure?title=AtmosphericPressure atmospheric pressure]</span> remains constant.


An example is a coffee-cup calorimeter, which is constructed from two nested  
An example is a coffee-cup calorimeter, which is constructed from two nested Styrofoam cups and a lid with two holes, allowing insertion of a thermometer and a stirring rod. The inner cup holds a known amount of a solute, usually water, that absorbs the heat from the reaction. When the reaction occurs, the outer cup provides insulation.<ref name="CCRConPresCalor">{{cite book |url=http://books.google.com/books?id=sorFoN-ne2EC&pg=PA226 |title=Chemistry and Chemical Reactivity |author=Kotz, John C.; Treichel, Paul M.; Townsend, John R. |publisher=Cengage Learning |year=2011 |page=226–227 |isbn=0840048289 |accessdate=11 May 2013}}</ref> Then:                
<span class="plainlinks">[http://en.wikipedia.org/wiki/Styrofoam?title=Styrofoam Styrofoam]</span> cups having holes through which a  
<span class="plainlinks">[http://en.wikipedia.org/wiki/Thermometer?title=Thermometer thermometer]</span> and a stirring rod can be inserted. The inner cup holds the solution in which of the reaction occurs, and the outer cup provides  
<span class="plainlinks">[http://en.wikipedia.org/wiki/Thermal_insulation?title=Insulation insulation]</span>. Then               


<math>Cp = \frac {W\Delta H}{M\Delta T}</math>
<math>Cp = \frac {W\Delta H}{M\Delta T}</math>


where
where...


:<math>Cp</math> = Specific heat at constant pressure
:<math>Cp</math> = Specific heat at constant pressure
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:<math>W</math> = mass of solute
:<math>W</math> = mass of solute
:<math>M</math> = molecular mass of solute
:<math>M</math> = molecular mass of solute
The measurement of heat using a simple calorimeter, like the coffee cup calorimeter, is an example of constant-pressure calorimetry, since the pressure (atmospheric pressure) remains constant during the process. Constant-pressure calorimetry is used in determining the changes in enthalpy occurring in solution. Under these conditions the change in enthalpy equals the heat.


==Differential scanning calorimeter==
==Differential scanning calorimeter==
''Main article:''<span class="plainlinks">[http://en.wikipedia.org/wiki/Differential_scanning_calorimetry?title=DifferentialScanningCalorimetry Differential scanning calorimetry]</span>.


In a '''differential scanning calorimeter''' (DSC),  
In a '''differential scanning calorimeter''' (DSC), heat flow into a sample—usually contained in a small aluminum capsule or 'pan'—is measured differentially, i.e., by comparing it to the flow into an empty reference pan.
<span class="plainlinks">[http://en.wikipedia.org/wiki/Heat_flow?title=HeatFlow heat flow]</span> into a sample—usually contained in a small  
<span class="plainlinks">[http://en.wikipedia.org/wiki/Aluminium?title=Aluminium aluminium]</span> capsule or 'pan'—is measured differentially, i.e., by comparing it to the flow into an empty reference pan.


In a '''<span class="plainlinks">[http://en.wikipedia.org/wiki/Heat_flux?title=HeatFlux heat flux]</span> DSC''', both pans sit on a small slab of material with a known (calibrated) heat resistance K. The temperature of the calorimeter is raised linearly with time (scanned), i.e., the heating rate  
In a '''[[heat flux]] DSC''', both pans sit on a small slab of material with a known (calibrated) heat resistance K. The temperature of the calorimeter is raised linearly with time (scanned), i.e., the heating rate  
dT/dt = β
dT/dt = β
is kept constant. This time linearity requires good design and good (computerized) temperature control. Of course, controlled cooling and isothermal experiments are also possible.
is kept constant. This time linearity requires good design and good (computerized) temperature control. Of course, controlled cooling and isothermal experiments are also possible.


Heat flows into the two pans by conduction. The flow of heat into the sample is larger because of its  
Heat flows into the two pans by conduction. The flow of heat into the sample is larger because of its heat capacity ''C<sub>p</sub>''. The difference in flow ''dq''/''dt'' induces a small temperature difference Δ''T'' across the slab. This temperature difference is measured using a thermocouple.<ref name="HöhneDiff03">{{cite book |url=http://books.google.com/books?id=tRt-Z5Duz7QC&pg=PA1 |title=Differential Scanning Calorimetry |author=Höhne, Günther; Hemminger, W.F.; Flammersheim, H.J. |publisher=Springer |year=2003 |page=1–7 |isbn=354000467X |accessdate=11 May 2013}}</ref> The heat capacity can in principle be determined from this signal:
<span class="plainlinks">[http://en.wikipedia.org/wiki/Heat_capacity?title=HeatCapacity heat capacity]</span> ''C<sub>p</sub>''. The difference in flow ''dq''/''dt'' induces a small temperature difference Δ''T'' across the slab. This temperature difference is measured using a  
<span class="plainlinks">[http://en.wikipedia.org/wiki/Thermocouple?title=Thermocouple thermocouple]</span>. The heat capacity can in principle be determined from this signal:


<math>\Delta T = K {dq\over dt} = K C_p\, \beta</math>
<math>\Delta T = K {dq\over dt} = K C_p\, \beta</math>


Note that this formula (equivalent to  
Note that this formula (equivalent to Newton's law of heat flow) is analogous to, and much older than, Ohm's law of electric flow:
<span class="plainlinks">[http://en.wikipedia.org/wiki/Law_of_heat_conduction?title=NewtonLaw Newton's law of heat flow]</span>) is analogous to, and much older than,  
<span class="plainlinks">[http://en.wikipedia.org/wiki/Ohm%27s_law?title=Ohm Ohm's law]</span> of electric flow:
ΔV = R dQ/dt = R I.
ΔV = R dQ/dt = R I.


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<math>{dq\over dt} = C_p \beta + f(t,T) </math>
<math>{dq\over dt} = C_p \beta + f(t,T) </math>


From the  
From the integral of this peak the enthalpy of melting can be determined, and from its onset the melting temperature.
<span class="plainlinks">[http://en.wikipedia.org/wiki/Integral?title=Integral integral]</span> of this peak the enthalpy of melting can be determined, and from its onset the melting temperature.


Differential scanning calorimetry is a workhorse technique in many fields, particularly in  
Differential scanning calorimetry is a workhorse technique in many fields, particularly in polymer characterization.
<span class="plainlinks">[http://en.wikipedia.org/wiki/Polymer?title=Polymer polymer]</span> characterization.


A '''modulated temperature differential scanning calorimeter''' (MTDSC) is a type of DSC in which a small oscillation is imposed upon the otherwise linear heating rate.
A '''modulated temperature differential scanning calorimeter''' (MTDSC) is a type of DSC in which a small oscillation is imposed upon the otherwise linear heating rate.
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This has a number of advantages. It facilitates the direct measurement of the heat capacity in one measurement, even in (quasi-)isothermal conditions. It permits the simultaneous measurement of heat effects that are reversible and not reversible at the timescale of the oscillation (reversing and non-reversing heat flow, respectively). It increases the sensitivity of the heat capacity measurement, allowing for scans at a slow underlying heating rate.
This has a number of advantages. It facilitates the direct measurement of the heat capacity in one measurement, even in (quasi-)isothermal conditions. It permits the simultaneous measurement of heat effects that are reversible and not reversible at the timescale of the oscillation (reversing and non-reversing heat flow, respectively). It increases the sensitivity of the heat capacity measurement, allowing for scans at a slow underlying heating rate.


'''Safety Screening''':- DSC may also be used as an initial safety screening tool.  In this mode the sample will be housed in a non-reactive crucible (often  
'''Safety Screening''':- DSC may also be used as an initial safety screening tool.  In this mode the sample will be housed in a non-reactive crucible (often gold, or gold-plated steel), and which will be able to withstand pressure (typically up to 100 bar). The presence of an exothermic event can then be used to assess the stability of a substance to heat. However, due to a combination of relatively poor sensitivity, slower than normal scan rates (typically 2-3°/min - due to much heavier crucible) and unknonwn [[activation energy]], it is necessary to deduct about 75-100°C from the initial start of the observed exotherm to '''suggest''' a maximum temperature for the material.  A much more accurate data set can be obtained from an adiabatic calorimeter, but such a test may take 2–3 days from ambient at a rate of 3°C increment per half hour.
<span class="plainlinks">[http://en.wikipedia.org/wiki/Gold?title=Gold Gold]</span>, or Gold plated steel), and which will be able to withstand  
<span class="plainlinks">[http://en.wikipedia.org/wiki/Pressure?title=Pressure pressure]</span> (typically up to 100
<span class="plainlinks">[http://en.wikipedia.org/wiki/Bar_(unit)?title=Bar bar]</span>). The presence of an  
<span class="plainlinks">[http://en.wikipedia.org/wiki/Exothermic?title=Exothermic exothermic]</span> event can then be used to assess the
<span class="plainlinks">[http://en.wikipedia.org/wiki/Chemical_stability?title=Stability stability]</span> of a substance to heat. However, due to a combination of relatively poor sensitivity, slower than normal scan rates (typically 2-3°/min - due to much heavier crucible) and unknonwn  
<span class="plainlinks">[http://en.wikipedia.org/wiki/Activation_energy?title=ActivationEnergy activation energy]</span>, it is necessary to deduct about 75-100°C from the initial start of the observed exotherm to '''suggest''' a maximum temperature for the material.  A much more accurate data set can be obtained from an adiabatic calorimeter, but such a test may take 2–3 days from
<span class="plainlinks">[http://en.wikipedia.org/wiki/Ambient_temperature?title=Ambient ambient]</span> at a rate of 3°C increment per half hour.


==Isothermal titration calorimeter==<!-- This section is linked from [[Titration]] -->
==Isothermal titration calorimeter==
''Main article:''<span class="plainlinks">[http://en.wikipedia.org/wiki/Isothermal_Titration_Calorimetry?title=ISC Isothermal Titration Calorimetry]</span>
In an '''isothermal
<span class="plainlinks">[http://en.wikipedia.org/wiki/Titration?title=Titration titration]</span> calorimeter''', the heat of reaction is used to follow a titration experiment. This permits determination of the mid point (
<span class="plainlinks">[http://en.wikipedia.org/wiki/Stoichiometry?title=Stoichiometry stoichiometry]</span>) (N) of a reaction as well as its enthalpy (delta H), entropy (delta S) and of primary concern the binding affinity (Ka)


The technique is gaining in importance particularly in the field of  
In an '''isothermal titration calorimeter''', the heat of reaction is used to follow a titration experiment. This permits determination of the midpoint (stoichiometry) (N) of a reaction as well as its enthalpy (delta H), entropy (delta S) and of primary concern the binding affinity (Ka).<ref name="PBIsoCalor">{{cite book |url=http://books.google.com/books?id=6h3In_GcIzEC&pg=PT312 |title=Physical Biochemistry: Principles and Applications |author=Sheehan, David |publisher=John Wiley & Sons |year=2009 |edition=2nd |page=296–99 |isbn=0470856025 |accessdate=11 May 2013}}</ref>
<span class="plainlinks">[http://en.wikipedia.org/wiki/Biochemistry?title=Biochemistry biochemistry]</span>, because it facilitates determination of substrate binding to
<span class="plainlinks">[http://en.wikipedia.org/wiki/Enzyme?title=Enzyme enzyme]</span>s. The technique is commonly used in the pharmaceutical industry to characterize potential drug candidates.


==See also==
The technique is gaining in importance, particularly in the field of biochemistry, because it facilitates determination of substrate binding to enzymes. The technique is commonly used in the pharmaceutical industry to characterize potential drug candidates.<ref name="PLIIso">{{cite book |url=http://books.google.com/books?id=0Jqe2I5SwbkC&pg=PA32 |title=Peptide-Lipid Interactions |author=Simon, Sidney A.; McIntosh, Thomas J. |publisher=Academic Press |year=2002 |page=32–33 |isbn=0080925855 |accessdate=11 May 2013}}</ref>
{{commons category|Calorimeters}}
*<span class="plainlinks">[http://en.wikipedia.org/wiki/Enthalpy?title=Enthalpy Enthalpy]</span>
*<span class="plainlinks">[http://en.wikipedia.org/wiki/Heat?title=Heat Heat]</span>
*<span class="plainlinks">[http://en.wikipedia.org/wiki/Calorie?title=Calorie Calorie]</span>
*<span class="plainlinks">[http://en.wikipedia.org/wiki/Heat_of_combustion?title=HeatOfCombustion Heat of combustion]</span>
*<span class="plainlinks">[http://en.wikipedia.org/wiki/Calorimeter_constant?title=CalorimeterConstant Calorimeter constant]</span>


==References==
==References==
<span class="plainlinks">[http://en.wikipedia.org/wiki/Calorimeter?title=WikipediaCalorimeter Wikipedia]</span>
<references />
 
 
{{Laboratory equipment}}


[[Category:Measuring instruments]]
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[[fr:Calorimètre]]
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[[id:Kalorimeter]]
[[it:Calorimetro]]
[[he:קלורימטר]]
[[ht:Kalorimèt]]
[[nl:Calorimeter]]
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[[pl:Kalorymetr]]
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Latest revision as of 18:11, 19 September 2021

The world’s first ice-calorimeter, used in the winter of 1782-83, by Antoine Lavoisier and Pierre-Simon Laplace, to determine the heat evolved in various chemical changes; calculations which were based on Joseph Black's prior discovery of latent heat. These experiments mark the foundation of thermochemistry.

A calorimeter (from Latin calor, meaning heat) is an object used for calorimetry, the process of measuring the heat of chemical reactions or physical changes as well as heat capacity. More specifically, a calorimeter handles the enthalpy changes of chemical reactions by thermally isolating the reaction system from its surroundings.[1] A simple calorimeter just consists of a thermometer attached to a metal container full of water suspended above a combustion chamber and is sometimes referred to as a "coffee cup" calorimeter, whereas more sophisticated forms like "flame" and "bomb" calorimeters involve combustion of the substance in a burner or pressurized vessel.

To find the enthalpy change per mole of a substance A in a reaction between two substances A and B, the substances are added to a calorimeter and the initial and final temperatures (before the reaction started and after it has finished) are noted. Multiplying the temperature change by the mass and specific heat capacities of the substances gives a value for the energy given off or absorbed during the reaction. Dividing the energy change by how many moles of A were present gives its enthalpy change of reaction. This method is used primarily in academic teaching as it describes the theory of calorimetry.[1] It does not account for the heat loss through the container or the heat capacity of the thermometer and container itself. In addition, the object placed inside the calorimeter shows that the objects transferred their heat to the calorimeter and into the liquid, and the heat absorbed by the calorimeter and the liquid is equal to the heat given off by the metals.[2]

History

In 1780, Antoine Lavoisier used a Guinea pig in his experiments with the calorimeter, a device used to measure heat production. The heat from the guinea pig's respiration melted snow surrounding the calorimeter, showing that respiratory gas exchange is a combustion, similar to a candle burning.[3]

Adiabatic calorimeters

An adiabatic calorimeter is a calorimeter used to examine a runaway reaction. Since the calorimeter runs in an adiabatic environment, any heat generated by the material sample under test causes the sample to increase in temperature, thus fueling the reaction.

No adiabatic calorimeter is adiabatic — some heat will be lost by the sample to the sample holder. A mathematical correction factor, known as the phi-factor, can be used to adjust the calorimetric result to account for these heat losses. The phi-factor is the ratio of the thermal mass of the sample and sample holder to the thermal mass of the sample alone.[4]

Reaction calorimeters

A reaction calorimeter is a calorimeter in which a chemical reaction is initiated within a closed insulated container. Reaction heats are measured and the total heat is obtained by integrating heat flow versus time. This is the standard used in industry to measure heats since industrial processes are engineered to run at constant temperatures. Reaction calorimetry can also be used to determine maximum heat release rate for chemical process engineering and for tracking the global kinetics of reactions.[5] There are four main methods for measuring the heat in reaction calorimeter:

Heat flow calorimetry

The cooling/heating jacket controls either the temperature of the process or the temperature of the jacket. Heat is measured by monitoring the temperature difference between heat transfer fluid and the process fluid. In addition fill volumes (i.e. wetted area), specific heat, heat transfer coefficient have to be determined to arrive at a correct value. It is possible with this type of calorimeter to do reactions at reflux, although the accuracy is not as good.[5]

Heat balance calorimeter

The cooling/heating jacket controls the temperature of the process. Heat is measured by monitoring the heat gained or lost by the heat transfer fluid.[5]

Power compensation

Power compensation uses a heater placed within the vessel to maintain a constant temperature. The energy supplied to this heater can be varied as reactions require and the calorimetry signal is purely derived from this electrical power.[5]

Constant flux

Constant flux calorimetry (or COFLUX as it is often termed) is derived from heat balance calorimetry and uses specialized control mechanisms to maintain a constant heat flow (or flux) across the vessel wall.

Bomb calorimeters

Bomb calorimeter
Bomb calorimeter

A bomb calorimeter is a type of constant-volume calorimeter used in measuring the heat of combustion of a particular reaction. Bomb calorimeters have to withstand the large pressure within the calorimeter as the reaction is being measured. Electrical energy is used to ignite the fuel; as the fuel is burning, it will heat up the surrounding air, which expands and escapes through a tube that leads the air out of the calorimeter. When the air is escaping through the copper tube it will also heat up the water outside the tube. The temperature of the water allows for calculating calorie content of the fuel.[4][1]

In more recent calorimeter designs, the whole bomb, pressurized with excess pure oxygen (typically at 30atm) and containing a weighed mass of a sample (typically 1-1.5 g) and a small fixed amount of water (to saturate the internal atmosphere, thus ensuring that all water produced is liquid, and removing the need to include enthalpy of vaporization in calculations), is submerged under a known volume of water (ca. 2000 ml) before the charge is electrically ignited. The bomb, with the known mass of the sample and oxygen, form a closed system - no gases escape during the reaction. The weighted reactant put inside the steel container is then ignited. Energy is released by the combustion and heat flow from this crosses the stainless steel wall, thus raising the temperature of the steel bomb, its contents, and the surrounding water jacket. The temperature change in the water is then accurately measured with a thermometer. This reading, along with a bomb factor (which is dependent on the heat capacity of the metal bomb parts), is used to calculate the energy given out by the sample burn. A small correction is made to account for the electrical energy input, the burning fuse, and acid production (by titration of the residual liquid). After the temperature rise has been measured, the excess pressure in the bomb is released.

Basically, a bomb calorimeter consists of a small cup to contain the sample, oxygen, a stainless steel bomb, water, a stirrer, a thermometer, the dewar or insulating container (to prevent heat flow from the calorimeter to the surroundings) and ignition circuit connected to the bomb. By using stainless steel for the bomb, the reaction will occur with no volume change observed.

Since there is no heat exchange between the calorimeter and surroundings → Q = 0 (adiabatic) ; no work performed → W = 0 Thus, the total internal energy change ΔU(total) = Q + W = 0

Also, total internal energy change ΔU(total) = ΔU(system) + ΔU(surroundings) = 0 → ΔU(system) = - ΔU(surroundings) = -Cv ΔT (constant volume → dV = 0)

where Cv = heat capacity of the bomb

Before the bomb can be used to determine heat of combustion of any compound, it must be calibrated. The value of Cv can be estimated by Cv (calorimeter) = m (water). Cv (water) + m (steel). Cv (steel)

m (water) and m (steel) can be measured;

Cv(water)= 1 cal/g.K

Cv(steel)= 0.1 cal/g.K

In laboratory, Cv is determined by running a compound with known heat of combustion value: Cv = Hc/ΔT

Common compounds are benzoic acid (Hc = 6318 cal/g) or p-methyl benzoic acid (Hc = 6957 cal/g).

Temperature (T) is recorded every minute and ΔT = T(final) - T(initial)

A small factor contributes to the correction of the total heat of combustion is the fuse wire. Nickel fuse wire is often used and has heat of combustion = 981.3 cal/g

In order to calibrate the bomb, a small amount (~ 1 g) of benzoic acid, or p-methyl benzoic acid is weighed. A length of Nickel fuse wire (~10 cm) is weighed both before and after the combustion process. Mass of fuse wire burned Δm = m(before) - m(after)

The combustion of sample (benzoic acid) inside the bomb ΔHc = ΔHc (benzoic acid) x m (benzoic acid) + ΔHc (Ni fuse wire) x Δm (Ni fuse wire)

ΔHc = Cv. ΔT → Cv = ΔHc/ΔT

Once Cv value of the bomb is determined, the bomb is ready to use to calculate heat of combustion of any compounds by ΔHc = Cv. ΔT[6]

Calvet-type calorimeters

The detection is based on a three-dimensional fluxmeter sensor. The fluxmeter element consists of a ring of several thermocouples in series. The corresponding thermopile of high thermal conductivity surrounds the experimental space within the calorimetric block. The radial arrangement of the thermopiles guarantees an almost complete integration of the heat. This is verified by the calculation of the efficiency ratio that indicates that an average value of 94% +/- 1% of heat is transmitted through the sensor on the full range of temperature of the Calvet-type calorimeter. In this setup, the sensitivity of the calorimeter is not affected by the crucible, the type of purge gas, or the flow rate. The main advantage of the setup is the increase of the experimental vessel's size and consequently the size of the sample, without affecting the accuracy of the calorimetric measurement.[7]

The calibration of the calorimetric detectors is a key parameter and has to be performed very carefully. For Calvet-type calorimeters, a specific calibration, so called Joule effect or electrical calibration, has been developed to overcome all the problems encountered by a calibration done with standard materials.

The main advantages of this type of calibration are as follows:

  • It is an absolute calibration.
  • The use of standard materials for calibration is not necessary. The calibration can be performed at a constant temperature, in the heating mode and in the cooling mode.
  • It can be applied to any experimental vessel volume.
  • It is a very accurate calibration.

An example of Calvet-type calorimeter is the C80 Calorimeter (reaction, isothermal and scanning calorimeter).[8]

Constant-pressure calorimeter

A constant-pressure calorimeter measures the change in enthalpy of a reaction occurring in solution during which the atmospheric pressure remains constant.

An example is a coffee-cup calorimeter, which is constructed from two nested Styrofoam cups and a lid with two holes, allowing insertion of a thermometer and a stirring rod. The inner cup holds a known amount of a solute, usually water, that absorbs the heat from the reaction. When the reaction occurs, the outer cup provides insulation.[9] Then:

where...

= Specific heat at constant pressure
= Enthalpy of solution
= Change in temperature
= mass of solute
= molecular mass of solute

The measurement of heat using a simple calorimeter, like the coffee cup calorimeter, is an example of constant-pressure calorimetry, since the pressure (atmospheric pressure) remains constant during the process. Constant-pressure calorimetry is used in determining the changes in enthalpy occurring in solution. Under these conditions the change in enthalpy equals the heat.

Differential scanning calorimeter

In a differential scanning calorimeter (DSC), heat flow into a sample—usually contained in a small aluminum capsule or 'pan'—is measured differentially, i.e., by comparing it to the flow into an empty reference pan.

In a heat flux DSC, both pans sit on a small slab of material with a known (calibrated) heat resistance K. The temperature of the calorimeter is raised linearly with time (scanned), i.e., the heating rate dT/dt = β is kept constant. This time linearity requires good design and good (computerized) temperature control. Of course, controlled cooling and isothermal experiments are also possible.

Heat flows into the two pans by conduction. The flow of heat into the sample is larger because of its heat capacity Cp. The difference in flow dq/dt induces a small temperature difference ΔT across the slab. This temperature difference is measured using a thermocouple.[10] The heat capacity can in principle be determined from this signal:

Note that this formula (equivalent to Newton's law of heat flow) is analogous to, and much older than, Ohm's law of electric flow: ΔV = R dQ/dt = R I.

When suddenly heat is absorbed by the sample (e.g., when the sample melts), the signal will respond and exhibit a peak.

From the integral of this peak the enthalpy of melting can be determined, and from its onset the melting temperature.

Differential scanning calorimetry is a workhorse technique in many fields, particularly in polymer characterization.

A modulated temperature differential scanning calorimeter (MTDSC) is a type of DSC in which a small oscillation is imposed upon the otherwise linear heating rate.

This has a number of advantages. It facilitates the direct measurement of the heat capacity in one measurement, even in (quasi-)isothermal conditions. It permits the simultaneous measurement of heat effects that are reversible and not reversible at the timescale of the oscillation (reversing and non-reversing heat flow, respectively). It increases the sensitivity of the heat capacity measurement, allowing for scans at a slow underlying heating rate.

Safety Screening:- DSC may also be used as an initial safety screening tool. In this mode the sample will be housed in a non-reactive crucible (often gold, or gold-plated steel), and which will be able to withstand pressure (typically up to 100 bar). The presence of an exothermic event can then be used to assess the stability of a substance to heat. However, due to a combination of relatively poor sensitivity, slower than normal scan rates (typically 2-3°/min - due to much heavier crucible) and unknonwn activation energy, it is necessary to deduct about 75-100°C from the initial start of the observed exotherm to suggest a maximum temperature for the material. A much more accurate data set can be obtained from an adiabatic calorimeter, but such a test may take 2–3 days from ambient at a rate of 3°C increment per half hour.

Isothermal titration calorimeter

In an isothermal titration calorimeter, the heat of reaction is used to follow a titration experiment. This permits determination of the midpoint (stoichiometry) (N) of a reaction as well as its enthalpy (delta H), entropy (delta S) and of primary concern the binding affinity (Ka).[11]

The technique is gaining in importance, particularly in the field of biochemistry, because it facilitates determination of substrate binding to enzymes. The technique is commonly used in the pharmaceutical industry to characterize potential drug candidates.[12]

References

  1. 1.0 1.1 1.2 Clugston, Michael J.; Flemming, Rosalind (2000). Advanced Chemistry. Oxford University Press. p. 148. ISBN 0199146330. http://books.google.com/books?id=qciCdSFpFPkC&pg=PA149. 
  2. Zumdahl, Steven S. (2009). Chemical Principles. Cengage Learning. p. 378–87. ISBN 061894690X. http://books.google.com/books?id=2OxrDtDaSqIC&pg=PA378. 
  3. Buchholz, Andrea C; Schoeller, Dale A. (2004). "Is a Calorie a Calorie?". American Journal of Clinical Nutrition 79 (5): 899S–906S. PMID 15113737. http://www.ajcn.org/cgi/content/full/79/5/899S. Retrieved 01 March 2013. 
  4. 4.0 4.1 Czichos, Horst ; Saito, Tetsuya; Smith, Leslie R., ed. (2006). Springer Handbook of Materials Measurement Methods. Springer. p. 410–414. ISBN 3540303006. http://books.google.com/books?id=8lANaR-Pqi4C&pg=PA410. Retrieved 08 May 2013. 
  5. 5.0 5.1 5.2 5.3 Maskill, Howard, ed. (2008). The Investigation of Organic Reactions and Their Mechanisms. John Wiley & Sons. p. 200–202. ISBN 0470994169. http://books.google.com/books?id=NgV9yqD-sOYC&pg=PA200. Retrieved 08 May 2013. 
  6. Polik, W. (1997). "Bomb Calorimetry". Hope College Chemistry Department. http://www.chem.hope.edu/~polik/Chem345-1997/calorimetry/bombcalorimetry1.html. Retrieved 01 March 2013. 
  7. Brown, Michael E., ed. (1998). Handbook of Thermal Analysis and Calorimetry: Principles and Practice. Elsevier. p. 619–629. ISBN 0080539599. http://books.google.com/books?id=33_3DBLGzMYC&pg=PR619. Retrieved 08 May 2013. 
  8. C80 "Calorimetry C-80". Setaram Instrumentation. http://www.setaram.com/C80.htm C80. Retrieved 01 March 2013. 
  9. Kotz, John C.; Treichel, Paul M.; Townsend, John R. (2011). Chemistry and Chemical Reactivity. Cengage Learning. p. 226–227. ISBN 0840048289. http://books.google.com/books?id=sorFoN-ne2EC&pg=PA226. Retrieved 11 May 2013. 
  10. Höhne, Günther; Hemminger, W.F.; Flammersheim, H.J. (2003). Differential Scanning Calorimetry. Springer. p. 1–7. ISBN 354000467X. http://books.google.com/books?id=tRt-Z5Duz7QC&pg=PA1. Retrieved 11 May 2013. 
  11. Sheehan, David (2009). Physical Biochemistry: Principles and Applications (2nd ed.). John Wiley & Sons. p. 296–99. ISBN 0470856025. http://books.google.com/books?id=6h3In_GcIzEC&pg=PT312. Retrieved 11 May 2013. 
  12. Simon, Sidney A.; McIntosh, Thomas J. (2002). Peptide-Lipid Interactions. Academic Press. p. 32–33. ISBN 0080925855. http://books.google.com/books?id=0Jqe2I5SwbkC&pg=PA32. Retrieved 11 May 2013.