For an ideal gas, internal energy depends only on what state variable?

Find \(\Delta U\) for \(1.0\,\mathrm{mol}\) of monatomic ideal gas warmed by \(10\,\mathrm{K}\).

A monatomic ideal gas cools by \(25\,\mathrm{K}\). Is \(\Delta U\) positive or negative?

Find the internal energy of \(2.0\,\mathrm{mol}\) of monatomic ideal gas at \(300\,\mathrm{K}\).

An ideal gas has \(n=3.0\,\mathrm{mol}\), \(C_V=20.8\,\mathrm{J\,mol^{-1}\,K^{-1}}\), and \(\Delta T=40\,\mathrm{K}\). Find \(\Delta U\).

A monatomic ideal gas expands isothermally. Find \(\Delta U\) and explain why volume change does not matter.

A monatomic ideal gas has pressure \(1.0\times10^5\,\mathrm{Pa}\) and volume \(0.060\,\mathrm{m^3}\). Find its internal energy.

For an ideal gas with \(f\) active quadratic degrees of freedom, derive \(C_V=fR/2\).

An ideal gas goes from \((p_i,V_i)\) to \((p_f,V_f)\). For a monatomic gas, derive \(\Delta U\) using only endpoint \(pV\) values.

Two ideal gases have the same \(n\) and same temperature change. Gas A is monatomic; gas B has \(f=5\). Compare their \(\Delta U\) values and interpret the result microscopically.