The average translational kinetic energy of ${N}_{2}$ gas molecules at $\ldots \ldots \ldots . .{ }^{\circ} {C}$ becomes equal to the ${K} . {E}$. of an electron accelerated from rest through a potential difference of $0.1$ $volt.$
$\left(\right.$ Given $\left.{k}_{{B}}=1.38 \times 10^{-23} \, {J} / {K}\right)$
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A spherical soap bubble inside an air chamber at pressure $P_0=10^5 Pa$ has a certain radius so that the excess pressure inside the bubble is $\Delta P=144 Pa$. Now, the chamber pressure is reduced to $8 P_0 / 27$ so that the bubble radius and its excess pressure change. In this process, all the temperatures remain unchanged. Assume air to be an ideal gas and the excess pressure $\Delta P$ in both the cases to be much smaller than the chamber pressure. The new excess pressure $\Delta P$ in $Pa$ is
$\frac{1}{2} $ mole of helium gas is contained in a container at $S.T.P.$ The heat energy needed to double the pressure of the gas, keeping the volume constant (specific heat of the gas $ = 3\,J\,g{m^{ - 1}}\,{K^{ - 1}})$ is ...... $J$
A container with insulating walls is divided into two equal parts by a partition fitted with a valve. One part is filled with an ideal gas at a pressure $P$ and temperature $T$, whereas the other part is completely evacuated. If the valve is suddenly opened, the pressure and temperature of the gas will be