An iron sphere having diameter $$D$$ and mass $$M$$ is immersed in hot water so that the temperature of the sphere increases by $$\delta T$$. If $$\alpha$$ is the coefficient of linear expansion of the iron then the change in the surface area of the sphere is

The work done by a Carnot engine operating between 300 K and 400 K is 400 J. The energy exhausted by the engine is

The slopes of the isothermal and adiabatic $$p-V$$ graphs of a gas are by $$S_I$$ and $$S_A$$ respectively. If the heat capacity ratio of the gas is $$\frac{3}{2}$$, then $$\frac{S_I}{S_A}=$$

The number of rotational degrees of freedom of a diatomic molecule