When a system is taken from state ' $a$ ' to state ' $c$ ' along a path abc, it is found that $\mathrm{Q}=80 \mathrm{cal}$ and $\mathrm{W}=35 \mathrm{cal}$. Along path adc $\mathrm{Q}=65 \mathrm{cal}$ the work done W along path adc is

The ratio of work done by an ideal rigid diatomic gas to the heat supplied by the gas in an isobaric process is

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?