The relation obeyed by a perfect gas during an adiabatic process is $$\mathrm{PV}^{3 / 2}$$. The initial temperature of the gas is '$$\mathrm{T}$$'. When the gas is compressed to half of its Initial volume, the final temperature of the gas is

A black rectangular surface of area '$$\mathrm{A}$$' emits energy '$$\mathrm{E}$$' per second at $$27^{\circ} \mathrm{C}$$. If length and breadth is reduced to $$(1 / 3)^{\text {rd }}$$ of its initial value and temperature is raised to $$327^{\circ} \mathrm{C}$$ then energy emitted per second becomes

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

A conducting rod of length $$1 \mathrm{~m}$$ has area of cross-section $$10^{-3} \mathrm{~m}^2$$. One end is immersed in baiting water $$\left(100^{\circ} \mathrm{C}\right)$$ and the other end in Ice $$\left(0^{\circ} \mathrm{C}\right)$$. If coefficient of thermal conductivity of $$\mathrm{rod}$$ is $$96 \mathrm{~cal} / \mathrm{sm}^{\circ} \mathrm{C}$$ and latent heat for ice is $$8 \times 10^{-4} \mathrm{cal} / \mathrm{kg}$$ then the amount of ice which will melt in one minute is