A gas is expanded from an initial state to a final state along a path on a $$p$$-$$V$$ diagram. The path consists of (i) an isothermal expansion of work 50 J , (ii) an adiabatic expansion and (iii) an isothermal expansion of work 20 J . If the internal energy of gas is changed by $$-$$30 J , then the work done by gas during adiabatic expansion is

The temperature of the sink of a Carnot engine is 250 K . In order to increase the efficiency of the Carnot engine from $$25 \%$$ to $$50 \%$$, the temperature of the sink should be increased by

In non-rigid diatomic molecule with an additional vibrational mode

A sphere of surface area $$4 \mathrm{~m}^2$$ at temperature 400 K and having emissivity 0.5 is located in an environment of temperature 200 K. The net rate of energy exchange of the sphere is (Stefan Boltzmann constant, $$\sigma=5.67 \times 10^{-8} \mathrm{Wm}^{-2} \mathrm{~K}^4)$$