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

A vessel containing 1 mole of $\mathrm{O}_2$ gas (molar mass 32) at temperature $T$. The pressure of the gas is $p$. An identical vessel containing one mole of He gas (molar mass 4) at temperature $4 T$ has a pressure of

A Carnot's heat engine works between the temperature $527^{\circ} \mathrm{C}$ and $127^{\circ} \mathrm{C}$. What amount of heat should it consume per second to deliver mechanical work at the rate of $1.0 \mathrm{~kW}$ ?

A monoatomic gas of molar mass m is kept in a insulated container. Container is moving with velocity v. If the container is suddenly stopped, then the change in the temperature of the gas is

One mole of an ideal diatomic gas undergoes a process as shown in the figure. The molar specific heat of the gas in the process is

An ideal monoatomic gas is taken round the cycle ABCDA as shown in the p-diagram

The work done during the cycle is

Which of the following graphs show the correct relation between conductivity and temperature for a metallic conductor?

The ratio of the specific heats ${{{C_v}} \over {{C_p}}} = {1 \over \gamma }$ in terms of degrees of freedom (n) is given by

A black body radiates energy at the rate E Wm^$-$2 at high temperature TK. When the temperature is reduced to $\left( {{T \over 4}} \right)$ K, the new radiant energy is

In an adiabatic process, where pressure is decreased by ${3 \over 4}$%, if ${{{C_p}} \over {{C_v}}} = {4 \over 3}$, then the volume increases by

A Carnot engine has the same efficiency between 600 K to 300 K and 1600 K to x K, then the value of x is

A vessel contains one mole of O₂ gas (molar mass 32) at a temperature T. The pressure of the gas is p. An identical vessel containing one mole of He gas (molar mass 4) at a temperature 2T has a pressure of

The figure shows graphs of pressure (p) versus density (d) for an ideal gas at two temperatures T₁ and T₂, then

When 2 moles of a monoatomic gas are mixed with 3 moles of a diatomic gas, the value of adiabatic exponent for the mixture is