_{i}= 10

^{5}Pa and volume V

_{i}= 10

^{-3}m

^{3}changes to a final state at P

_{f}= $$\left( {{1 \over {32}}} \right) \times {10^5}\,Pa$$ and V

_{f}= 8 $$ \times $$ 10

^{-3}m

^{3}in an adiabatic quasi-static process, such that P

^{3}V

^{5}= constant. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at P

_{i}followed by an isochoric (isovolumetric) process at volume V

_{f}. The amount of heat supplied to the system in the two-step process is approximately

The temperature of water fed into the device cannot exceed 30°C and the entire stored 120 litres of water is initially cooled to 10°C. The entire system is thermally insulated. The minimum value of P (in watts) for which the device can be operated for 3 hours is :

(Specific heat of water is 4.2 kJ kg

^{−1}K

^{−1}and the density of water is 1000 kg m

^{−3})

^{–2}are incident on a spherical black body kept in surroundings of temperature 300 K. Take Stefan-Boltzmann constant $$\sigma $$ = 5.7 $$ \times $$ 10

^{–8}Wm

^{–2}K

^{–4}and assume that the energy exchange with the surroundings is only through radiation. The final steady state temperature of the black body is close to

In the figure a container is shown to have a movable (without friction) piston on top. The container and the piston are all made of perfectly insulating material allowing no heat transfer between outside and inside the container. The container is divided into two compartments by a rigid partition made of a thermally conducting material that allows slow transfer of heat. The lower compartment of the container is filled with 2 moles of an ideal monatomic gas at 700 K and the upper compartment is filled with 2 moles of an ideal diatomic gas at 400 K. The heat capacities per mole of an ideal monatomic gas are $${C_v} = {3 \over 2}R$$, $${C_p} = {5 \over 2}R$$, and those for an ideal diatomic gas are $${C_v} = {5 \over 2}R$$, $${C_p} = {7 \over 2}R$$.

Consider the partition to be rigidly fixed so that it does not move. When equilibrium is achieved, the final temperature of the gases will be