The efficiency of a Carnot's engine is $25 \%$. When the temperature of sink is 300 K . The increase in the temperature of source required for the efficiency to become $50 \%$ is

When 100 J of heat is supplied to a gas, the increase in the internal energy of the gas is 60 J . Then the gas is /can

An ideal gas is kept in a cylinder of volume $3 \mathrm{~m}^3$ at a pressure of $3 \times 10^5 \mathrm{~Pa}$. The energy of the gas is

The temperature difference across two cylindrical rods $A$ and $B$ of same material and same mass are $40^{\circ} \mathrm{C}$ and $60^{\circ} \mathrm{C}$ respectively. In steady state, if the rates of flow of heat through the rods $A$ and $B$ are in the ratio 3:8, the ratio of the length of the rods $A$ and $B$ is