The two ends of a rod of length ' $x$ ' and uniform cross-sectional area ' A ' are kept at temperatures ' $\mathrm{T}_1$ ' and ' $\mathrm{T}_2$ ' respectively ( $\mathrm{T}_1>\mathrm{T}_2$ ). If the rate of heat transfer is ' $\mathrm{Q} / \mathrm{t}$ ', through the rod in steady state, then the coefficient of thermal conductivity ' K ' is

When the pressure of the gas contained in a closed vessel is increased by $2.3 \%$, the temperature of the gas increases by 4 K . The initial temperature of the gas is

Black bodies A and B radiate maximum energy with wavelength difference $4 \mu \mathrm{~m}$. The absolute temperature of body A is 3 times that of B. The wavelength at which body $B$ radiates maximum energy is

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