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, $$\sigma=5.67 \times 10^{-8} \mathrm{Wm}^{-2} \mathrm{~K}^4)$$

A Carnot engine operates between a source and a sink. The efficiency of the engine is $$40 \%$$ and the temperature of the sink is $$27^{\circ} \mathrm{C}$$. If the efficiency is to be increased to $$50 \%$$, then the temperature of the source must be increased by