A gas undergoes a change in which its pressure ' P ' and volume ' V ' are related as $\mathrm{PV}^{\mathrm{n}}=$ constant, where n is a constant. If the specific heat of the gas in this change is zero, then the value of $n$ is ( $\gamma=$ adiabatic ratio)

Hot water cools from $80^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$ in 1 minutes. In cooling from $60^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C}$ it will take (room temperature $=30^{\circ} \mathrm{C}$ )

A Carnot engine has efficiency $\frac{1}{6}$. It becomes $\frac{1}{3}$, when the temperature of $\operatorname{sink}$ is lowered by

57 K . The temperature of the source is

The r.m.s. speed of gas molecules at 800 K will be