A sphere is at temperature 600 K . In an external environment of 200 K , its cooling rate is ' $R$ ' When the temperature of the sphere falls to 400 K , then cooling rate ' $R$ ' will become

A gas expands in such a way that its pressure and volume satisfy the condition $\mathrm{PV}^2=$ constant. Then the temperature of the gas

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