A gas at absolute temperature $300 \mathrm{K}$ has pressure $p=4\times {10}^{-10} \mathrm{N} {\mathrm{m}}^{-2}$. Boltzmann constant $k=1.38\times {10}^{-23} \mathrm{J} {\mathrm{K}}^{-1}$. The number of molecules per ${\mathrm{cm}}^3$ is of the order of

A cylindrical steel plug is inserted into a circular hole of diameter $2.60 \mathrm{cm}$ in a brass plate. When the plug and the plates are at a temperature of $20 °\mathrm{C},$ the diameter of the plug is $0.010 \mathrm{cm}$ smaller than that of the hole. The temperature at which the plug will just fit in it is 

$\left(\mathrm{Given},{\alpha }_{\mathrm{steel}}=\frac{11\times {10}^{-6}}{{}^{\circ }\mathrm{C}} \mathrm{and} {\alpha }_{\mathrm{brass}}=\frac{19\times {10}^{-6}}{{}^{\circ }\mathrm{C}}\right)\le \le$

$p-V$ diagram was obtained from state $1$ to state $2$ when a given mass of a gas is subjected to temperature changes. During this process, the gas is