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Difference between revisions of "Molar heat capacity"

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Adding heat to a substance changes its temperature in accordance to <cmath>\Delta Q=nc_M\Delta T</cmath>
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The molar heat capacity is the amount of energy required to change the temperature of an amount of substance by a certain amount per moles of the substance and change in temperature.
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<math>\Delta Q=</math> change in heat
 
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<math>n=</math> moles of substance
 
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<math>c_M=</math> molar heat capacity
 
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<math>\Delta T=</math> change in temperature
 
  
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At constant volume, <math>c_M=c_V</math>.
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Adding [[heat]] to a substance changes its temperature in accordance to <cmath>\Delta Q=nc_M\Delta T,</cmath>
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At constant pressure, <math>c_M=c_P</math>.
 
  
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For an ideal gas, <math>c_P=c_V+R</math>.
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where
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For an incompressible substance, <math>c_P=c_V</math>.
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<math>\Delta Q</math> is the change in heat, <math>n</math> is the number of moles of substance, <math>c_M</math> is the molar heat capacity, and
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<math>\Delta T</math> is the change in temperature.
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At constant volume, <math>c_M=c_V</math>. At constant pressure, <math>c_M=c_P</math>.
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For an ideal gas, <math>c_P=c_V+R</math> where <math>R=</math> the ideal gas constant. For an incompressible substance, <math>c_P=c_V</math>.
  
 
In adiabatic compression (<math>\Delta Q=0</math>) of an ideal gas, <math>PV^\gamma</math> stays constant, where <math>\gamma=\frac{c_V+R}{c_V}</math>.
 
In adiabatic compression (<math>\Delta Q=0</math>) of an ideal gas, <math>PV^\gamma</math> stays constant, where <math>\gamma=\frac{c_V+R}{c_V}</math>.
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== See Also ==
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*An excellent derivation of the last equation can be found [https://www.animations.physics.unsw.edu.au/jw/Adiabatic-expansion-compression.htm here].
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* [[Heat]]
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* [[Thermodynamics]]
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[[Category: Physics]]
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Latest revision as of 11:02, 1 August 2020

The molar heat capacity is the amount of energy required to change the temperature of an amount of substance by a certain amount per moles of the substance and change in temperature.

Adding heat to a substance changes its temperature in accordance to \[\Delta Q=nc_M\Delta T,\]

where $\Delta Q$ is the change in heat, $n$ is the number of moles of substance, $c_M$ is the molar heat capacity, and $\Delta T$ is the change in temperature.

At constant volume, $c_M=c_V$. At constant pressure, $c_M=c_P$.

For an ideal gas, $c_P=c_V+R$ where $R=$ the ideal gas constant. For an incompressible substance, $c_P=c_V$.

In adiabatic compression ($\Delta Q=0$) of an ideal gas, $PV^\gamma$ stays constant, where $\gamma=\frac{c_V+R}{c_V}$.

See Also

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