The r.m.s. velocity of gas molecules kept at temperature $27^{\circ} \mathrm{C}$ in a vessel is $61 \mathrm{~m} / \mathrm{s}$. Molecular weight of gas is nearly

$$\left[\mathrm{R}=8.31 \frac{\mathrm{~J}}{\mathrm{~mol} \mathrm{~K}}\right]$$

A diatomic gas undergoes adiabatic change. Its pressure P and temperature T are related as $\mathrm{P} \propto \mathrm{T}^{\mathrm{x}}$ where the value of x is

A monoatomic gas is heated at constant pressure. The percentage of total heat used for doing external work is

Two rods, one of copper ( Cu$)$ and the other of iron ( Fe ) having initial lengths $\mathrm{L}_1$ and $\mathrm{L}_2$ respectively are connected together to form a single rod of length $L_1+L_2$. The coefficient of linear expansion of Cu and Fe are $\alpha_c$ and $\alpha_i$ respectively. If the length of each rod increases by the same amount when their temperatures are raised by $t^{\circ} \mathrm{C}$, then ratio of $\frac{L_1-L_2}{L_1+L_2}$ will be