Initially,a gas of diatomic molecules is contained in a cylinder of volume $V_{1}$ at a pressure $P_{1}$ and temperature $250\, K$. Assuming that $25\%$ of the molecules get dissociated,causing a change in the number of moles. The pressure of the resulting gas at temperature $2000\, K$,when contained in a volume $2V_{1}$,is given by $P_{2}$. The ratio $\frac{P_{2}}{P_{1}}$ is:

$0.056 \, kg$ of Nitrogen is enclosed in a vessel at a temperature of $127 \, ^{\circ}C$. The amount of heat required to double the speed of its molecules is $k \, cal$. (Take $R = 2 \, cal \, mole^{-1} K^{-1}$)

$A$ cylindrical tube $AB$ of length $l$, closed at both ends, contains an ideal gas of $1 \text{ mol}$ having molecular weight $M$. The tube is rotated in a horizontal plane with constant angular velocity $\omega$ about an axis perpendicular to $AB$ and passing through the edge at end $A$. If $P_{A}$ and $P_{B}$ are the pressures at $A$ and $B$ respectively, then (Consider the temperature is same at all points in the tube):

Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains neon (monatomic),the second contains chlorine (diatomic),and the third contains uranium hexafluoride (polyatomic). Do the vessels contain equal number of respective molecules? Is the root mean square speed of molecules the same in the three cases? If not,in which case is $v_{rms}$ the largest?

Two rigid boxes containing different ideal gases are placed on a table. Box $A$ contains one mole of nitrogen at temperature $T_0$,while Box $B$ contains one mole of helium at temperature $(7/3)T_0$. The boxes are then put into thermal contact with each other,and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of the boxes). The final temperature of the gases,$T_f$,in terms of $T_0$ is:

Which of the following statements about the kinetic theory of gases is wrong?