5 g of ice at $$-30^{\circ} \mathrm{C}$$ and 20 g of water at $$35^{\circ} \mathrm{C}$$ are mixed together in a calorimeter. The final temperature of the mixture is (Neglect heat capacity of the calorimeter, specific heat capacity of ice $$=0.5 \mathrm{cal} \mathrm{g}^{-1}{ }^{\circ} \mathrm{C}^{-1}$$ and latent heat of fusion of ice $$=80 \mathrm{cal} \mathrm{g}^{-1}$$ and specific heat. capacity of water $$=1 \mathrm{cal} \mathrm{g}^{-1}{ }^{\circ} \mathrm{C}^{-1}$$)

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 $$\frac{S_I}{S_A}=$$