$A$ 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 undergoing a constant temperature process (isothermal process),what is the nature of the graph between pressure $(P)$ and $\frac{1}{V}$ (where $V$ is volume)?

State and explain Dalton's law of partial pressure.

$A$ sample of $O_2$ gas has a volume of $100 \ ml$ at a pressure of $1 \ atm$ and a temperature of $27^{\circ}C$. If the pressure is increased to $2 \ atm$ while the volume remains $100 \ ml$,the new temperature will be .... $^{\circ}C$.

$A$ 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 $K$.

The air density at Mount Everest is less than that at the sea level. It is found by mountaineers that for one trip lasting a few hours,the extra oxygen needed by them corresponds to $30,000 \, cc$ at sea level (pressure $1 \, atm$,temperature $27^{\circ}C$). Assuming that the temperature around Mount Everest is $-73^{\circ}C$ and that the oxygen cylinder has a capacity of $5.2 \, L$,the pressure at which $O_2$ must be filled (at site) in the cylinder is .... $atm$.