A certain gas occupies \(0.1 \mathrm{~m}^{3}\) at 1 bar pressure. It is compressed adiabatically to a pressure of \(7 \mathrm{bar}\). Find the new volume, and change in internal energy. The density of gas at \(0^{\circ} \mathrm{C}\) and \(1 \mathrm{bar}\) is \(1.5 \mathrm{~kg} / \mathrm{m}^{3}\). Take \(c_{v}=0.728 \mathrm{~kJ} / \mathrm{kg}\). \(K\).