The internal energy of an ideal diatomic gas corresponding to volume ' $V$ ' and pressure ' P ' is 2.5 PV. The gas expands from 1 litre to 2 litre at a constant pressure of $10^5 \mathrm{~N} / \mathrm{m}^2$. The heat supplied to a gas is

Four moles of hydrogen, two moles of helium and one mole of water vapour form an ideal gas mixture. $\left[C_{\mathrm{v}}\right.$ for hydrogen $=\frac{5}{2} R, C_v$ for helium $=\frac{3}{2} R, \quad C_{\mathrm{v}}$ for water vapour $\left.=3 \mathrm{R}\right]$ What is the molar specific heat at constant pressure of the mixture?

A sheet of steel is 40 cm long and 5 cm broad at $0^{\circ} \mathrm{C}$. The surface area of the sheet increases by $1.4 \mathrm{~cm}^2$ at $100^{\circ} \mathrm{C}$. Coefficient of linear expansion of steel is

A quantity of heat ' $Q$ ' is supplied to monoatomic ideal gas which expands at constant pressure. The fraction of heat converted into work is $\left[\gamma=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\frac{5}{3}\right]$