Two vessels of equal volume contain the same gas. Their pressures and temperatures are $P_1, T_1$ and $P_2, T_2$ respectively. When they are connected,the common pressure and temperature are $P$ and $T$. Then $P/T$ is equal to:

The ratio $C_P / C_V$ for a gas mixture consisting of $8 \ g$ of helium and $16 \ g$ of oxygen is

The speed of sound in hydrogen at $NTP$ is $1270 \, m/s$. Then,the speed in a mixture of hydrogen and oxygen in the ratio $4 : 1$ by volume will be ..... $m/s$.

$A$ closed container of volume $0.02 \ m^3$ contains a mixture of neon and argon gases at a temperature of $27^{\circ}C$ and a pressure of $1 \times 10^5 \ N/m^2$. The total mass of the mixture is $28 \ g$. If the atomic weights of neon and argon are $20$ and $40$ respectively,find the mass of each gas in the container in $g$,assuming they behave as ideal gases. $(R = 8.314 \ J/mol \cdot K)$

Sound travels in a mixture of $2$ moles of helium and $n$ moles of hydrogen. If the root-mean-square (rms) speed of gas molecules in the mixture is $\sqrt{2}$ times the speed of sound,then the value of $n$ will be:

If $2 \text{ moles}$ of an ideal monoatomic gas at a temperature of $27^{\circ} C$ is mixed with $4 \text{ moles}$ of another ideal monoatomic gas at a temperature of $327^{\circ} C$,then the temperature of the mixture of the two gases is: (in $^{\circ} C$)