A monoatomic ideal gas, initially at temperature $\mathrm{T}_1$ is enclosed in a cylinder fitted with massless, frictionless piston. By releasing the piston suddenly, the gas is allowed to expand adiabatically to a temperature $\mathrm{T}_2$. If $\mathrm{L}_1$ and $\mathrm{L}_2$ are the lengths of the gas columns before and after expansion respectively, then $\left(T_2 / T_1\right)$ is given by

A coil has inductance 2 H . The ratio of its reactance when it is connected first to an a.c. source and then to a d.c. source is

In n-type semiconductor, free electrons donated by the impurity atoms occupy energy levels in

Two bodies A and B at temperatures ' $\mathrm{T}_1$ ' K and ' $\mathrm{T}_2$ ' K respectively have the same dimensions. Their emissivities are in the ratio $16: 1$. At $\mathrm{T}_1=\mathrm{xT}_2$, they radiate the same amount of heat per unit area per unit time. The value of $x$ is