During a reversible adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $\frac{C_p}{C_V}$ for the gas is:

At $298 \, K$ temperature,$4 \, g$ of $H_2$ gas is filled in a $500 \, mL$ vessel. Due to a small hole in the vessel,after some time,the pressure in the vessel becomes $50 \, bar$. Find the number of $H_2$ molecules that have escaped from the vessel? $(R = 8.314 \times 10^{-2} \, L \, bar \, mol^{-1} \, K^{-1})$

$A$ gas occupies $10 \ L$ at $0 \ ^{\circ}C$ and $2 \ atm$ pressure. At what temperature will the pressure in the container be $2.5 \ atm$,assuming the volume remains constant (in $^{\circ}C$)?

Two vessels are filled with ideal gases $A$ and $B$ and are connected through a pipe of zero volume as shown in the figure. The stop cock is opened and the gases are allowed to mix homogeneously and the temperature is kept constant. The partial pressures of $A$ and $B$ respectively (in $atm$) are:

Two separate bulbs contain ideal gases $A$ and $B$. The density of gas $A$ is twice that of gas $B$. The molecular mass of $A$ is half that of gas $B$. The two gases are at the same temperature. The ratio of the pressure of $A$ to that of gas $B$ is

At $300 \ K$,$22 \ g$ of $CO_2$ gas exerts a pressure of $5 \ atm$. What is the volume of the gas at the same temperature (in $dm^3$)? $(R = 0.0821 \ L \ atm \ K^{-1} \ mol^{-1})$