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The change in volume $V$ with respect to an increase in pressure $P$ has been shown in the figure for a non-ideal gas at four different temperatures ${T_1},\,{T_2},\,{T_3}$ and ${T_4}$. The critical temperature of the gas is
A cylinder of capacity $20$ litres is filled with ${H_2}$ gas. The total average kinetic energy of translatory motion of its molecules is $1.5 \times {10^5}\,J$. The pressure of hydrogen in the cylinder is
A container is divided into two chambers by a partition. The volume of first chamber is $4.5$ litre and second chamber is $5.5$ litre. The first chamber contain $3.0$ moles of gas at pressure $2.0\, atm$ and second chamber contain $4.0$ moles of gas at pressure $3.0\, atm$ .After the partition is removed and the mixture attains equilibrium, then, the common equilibrium pressure existing in the mixture is $x \times 10^{-1} atm$. Value of $x$ is.........
$Assertion$: The total translational kinetic energy of all the molecules of a given mass of an ideal gas is $1.5\, times$ the product of its pressure and its volume.
$Reason$ : The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.
The pressure $P$ of an ideal diatomic gas varies with its absolute temperature $T$ as shown in figure. The molar heat capacity of gas during this process is ........... $R$ [$R$ is gas constant]
Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as $V ^q$, where $V$ is the volume of the gas. The value of $q$ is $\left( {\gamma = \frac{{{C_P}}}{{{C_V}}}} \right)$