A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure P_i = 10⁵ Pa and volume V_i = 10^-3 m³ changes to a final state at P_f = $$\left( {{1 \over {32}}} \right) \times {10^5}\,Pa$$ and V_f = 8 $$ \times $$ 10^-3 m³ in an adiabatic quasi-static process, such that P³V⁵ = 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 ends Q and R of two thin wires, PQ and RS, are soldered (joined) together. Initially each of the wires has a length of 1 m at 10^oC. Now the end P is maintained at 10^oC, while the end S is heated and maintained at 400^oC. The system is thermally insulated from its surroundings. If the thermal conductivity of wire PQ is twice that of the wire RS and the coefficient of linear thermal expansion of PQ is 1.2 $$ \times $$ 10^-5 K^-1 , the change in length of the wire PQ is

A water cooler of storage capacity 120 litres can cool water at a constant rate of P watts. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates constantly 3 kW of heat (thermal load).
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)

Parallel rays of light of intensity $$I$$ = 912 Wm^–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^–2K^–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