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# 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.