Molar heat capacity
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 ![\[\Delta Q=nc_M\Delta T,\]](http://latex.artofproblemsolving.com/1/3/a/13a7fd6bf5581fdc8e7807b49fb2bfc822c3bfc6.png)
where
is the change in heat, 
is the number of moles of substance, 
is the molar heat capacity, and
is the change in temperature.
At constant volume, 
. At constant pressure, 
.
For an ideal gas, 
where 
the ideal gas constant. For an incompressible substance, 
.
In adiabatic compression (
) of an ideal gas, 
stays constant, where 
.
See Also
- An excellent derivation of the last equation can be found here.
- Heat
- Thermodynamics
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