For an ideal gas, which is larger: \(C_P\) or \(C_V\)?

State Mayer's relation for an ideal gas.

A gas has \(C_V=12.5\,\mathrm{J\,mol^{-1}\,K^{-1}}\). Find \(C_P\).

A gas has \(C_P=29.1\,\mathrm{J\,mol^{-1}\,K^{-1}}\) and \(C_V=20.8\,\mathrm{J\,mol^{-1}\,K^{-1}}\). Find \(\gamma\).

Find the heat needed to raise \(2.0\,\mathrm{mol}\) of ideal gas by \(30\,\mathrm{K}\) at constant volume if \(C_V=20.8\,\mathrm{J\,mol^{-1}\,K^{-1}}\).

For the same gas in the previous question, find the heat needed at constant pressure.

For a monatomic ideal gas, derive \(C_P\) and \(\gamma\) from \(C_V=3R/2\).

A gas has \(\gamma=1.40\). Derive \(C_V\) and \(C_P\) in terms of \(R\).

Show from the first law why \(C_P-C_V=R\) for an ideal gas.

An ideal gas is heated through \(\Delta T\) at constant pressure. Derive the fraction of the heat input that becomes expansion work in terms of \(\gamma\).