During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of $$\frac{\mathrm{Cp}}{\mathrm{Cv}}$$ for the gas is :

The equation of state of a real gas is given by $$\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$$, where $$\mathrm{P}, \mathrm{V}$$ and $$\mathrm{T}$$ are pressure, volume and temperature respectively and $$\mathrm{R}$$ is the universal gas constant. The dimensions of $$\frac{\mathrm{a}}{\mathrm{b}^2}$$ is similar to that of :

The total kinetic energy of 1 mole of oxygen at $$27^{\circ} \mathrm{C}$$ is : [Use universal gas constant $$(R)=8.31 \mathrm{~J} /$$ mole K]

$$0.08 \mathrm{~kg}$$ air is heated at constant volume through $$5^{\circ} \mathrm{C}$$. The specific heat of air at constant volume is $$0.17 \mathrm{~kcal} / \mathrm{kg}^{\circ} \mathrm{C}$$ and $$\mathrm{J}=4.18$$ joule/$$\mathrm{~cal}$$. The change in its internal energy is approximately.