Two moles of an ideal monoatomic gas undergo a cyclic process as shown in figure. The temperatures in different states are given as $6 \mathrm{~T}_1=3 \mathrm{~T}_2=2 \mathrm{~T}_4=\mathrm{T}_3=2400 \mathrm{~K}$. The work done by the gas during the complete cycle is ( $\mathrm{R}=$ Universal gas constant)

Two spherical black bodies have radii ' $R_1$ ' and ' $R_2$ '. Their surface temperatures are $T_1 K$ and $T_2 K$ respectively. If they radiate the same power, the ratio $\frac{R_1}{R_2}$ is

A thermometer bulb has volume $10^{-6} \mathrm{~m}^3$ and cross-section of the stem is $0.002 \mathrm{~cm}^2$. The bulb is filled with mercury at $0^{\circ} \mathrm{C}$. If the thermometer reads temperature as $100^{\circ} \mathrm{C}$, then the length of mercury column is (coefficient of cubical expansion of mercury $=18 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ )

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