The relation between internal energy $U$,pressure $P$,and volume $V$ for an ideal gas is given by $U = 2 + 2PV$. The gas is:

$A$ gas mixture consists of $3$ moles of oxygen and $5$ moles of argon at temperature $T$. Assuming the gases to be ideal and the oxygen bond to be rigid,the total internal energy (in units of $RT$) of the mixture 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 ..... $m/s$.

Three ideal gases at absolute temperatures $T_1, T_2,$ and $T_3$ are mixed. The number of molecules are $n_1, n_2,$ and $n_3$ respectively. Assuming no loss of energy,what is the final temperature of the mixture?

If the speed of sound in a mixture of $2$ moles of Helium and $2$ moles of Hydrogen at temperature $\frac{972}{5} \,K$ is $n \times 100 \,ms^{-1}$, then the value of $n$ is (Take, $R=\frac{25}{3} \,J \,mol^{-1} \,K^{-1}$)

If $4$ moles of an ideal monoatomic gas at temperature $400 \,K$ is mixed with $2$ moles of another ideal monoatomic gas at temperature $700 \,K$, the temperature of the mixture is: