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

For an ideal gas with pressure $P$,temperature $T$,and volume $V$,where the mass of each molecule is $m$,what is the density of the gas? ($k$ is the Boltzmann constant)

Air is filled at $60^oC$ in a vessel with an open mouth. The vessel is heated to a temperature $T$ so that $1/4^{th}$ of the air escapes. Assuming the volume of the vessel remains constant,the value of $T$ is ....... $^oC$.

$A$ monoatomic ideal gas of two moles is taken through a cyclic process starting from $1$ as shown. Given $\frac{V_2}{V_1} = 2$ and $\frac{V_4}{V_1} = 4$. The temperature at state $1$ is $T_1 = 27\,^oC$. Find the temperature at state $2$,i.e.,$T_2$ in $K$.

$A$ container of fixed volume contains a gas at $27^{\circ} C$. To double the pressure of the gas,the temperature of the gas should be raised to . . . . . . ${ }^{\circ} {C}$.

$A$ cylinder containing gas at $27\,^{\circ}C$ is divided into two parts of equal volume,each $100\,cm^3$,and at equal pressure by a piston of cross-sectional area $10.85\,cm^2$. The gas in one part is raised in temperature to $100\,^{\circ}C$ while the other is maintained at the original temperature. The piston and walls are perfect insulators. How far will the piston move during the change in temperature? (in $cm$)