A metal sphere cools at the rate of $$1.5^{\circ} \mathrm{C} / \mathrm{min}$$ when its temperature is $$80^{\circ} \mathrm{C}$$. At what rate will it cool when its temperature falls to $$50^{\circ} \mathrm{C}$$. [Temperature of surrounding is $$30^{\circ} \mathrm{C}$$]

A monoatomic gas is suddenly compressed to $$(1 / 8)^{\text {th }}$$ of its initial volume adiabatically. The ratio of the final pressure to initial pressure of the gas is $$(\gamma=5 / 3)$$

A monoatomic ideal gas initially at temperature $$\mathrm{T}_1$$ is enclosed in a cylinder fitted with 8 frictionless piston. The gas is allowed to expand adiabatically to a temperature $$\mathrm{T}_2$$ by releasing the piston suddenly. $$\mathrm{L}_1$$ and $$\mathrm{L}_2$$ are the lengths of the gas columns before and after the expansion respectively. Then $$\frac{\mathrm{T}_2}{\mathrm{~T}_1}$$ is

For a monoatomic gas, the work done at constant pressure is '$$\mathrm{W}$$' The heat supplied at constant volume for the same rise in temperature of the gas is

$$[\gamma=\frac{C_p}{C_v}=\frac{5}{2}$$ for monoatomic gas]