Molar heat capacity

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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, $c_P=c_V+R$. For an incompressible substance, $c_P=c_V$.

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

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