Molar heat capacity

Adding heat to a substance changes its temperature in accordance to $\Delta Q=nc_M\Delta T$ $\Delta Q=$ change in heat
$n=$ moles of substance
$c_M=$ molar heat capacity
$\Delta T=$ 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 $\gamma=\frac{c_V+R}{c_V}$ . An excellent derivation of this can be found here.

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Molar heat capacity