A Carnot engine has an efficiency of $\frac{1}{6}$. When the temperature of sink is reduced by 62 K , its efficiency is doubled. The temperature of the source is

If the r.m.s. velocity of gas is V at temperature T , then

In resistance thermometer, the resistance at $0^{\circ} \mathrm{C}$ and $100^{\circ} \mathrm{C}$ are $6.74 \Omega$ and $7.74 \Omega$ respectively. The temperature corresponding to $6.53 \Omega$ resistance is

An ideal gas in a container of volume 500 cc is at a pressure of $2 \times 10^5 \mathrm{~N} / \mathrm{m}^2$. The average kinetic energy of each molecule is $6 \times 10^{-21} \mathrm{~J}$. The number of gas molecules in the container is