A cylinder of radius $R$ made of a material of thermal conductivity $k_1$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2 R$ made of a material of thermal conductivity $k_2$. The two ends of a combined system are maintained at two different temperature. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is

In a certain process, 400 cal of heat is supplied to a system and at the same time 105 J of mechanical work was done on the system. The increase in its internal energy is

Two rods $P$ and $Q$ have equal lengths. Their thermal conductivities are $K_1$ and $K_2$ and cross-sectional areas are $A_1$ and $A_2$. When the temperature at ends of each rod are $T_1$ and $T_2$ respectively, the rate of flow of heat through $P$ and $Q$ will be equal, if

In the given cycle $ A B C D A $, the heat required for an ideal monoatomic gas will be