Match Column - I and Column - II and choose the correct match from the given choices.
 

	Column - I		Column - II
(A)	root mean square speed of gas molecules	(P)	\(\frac13nm\bar v^2\)
(B)	the pressure exerted by an ideal gas	(Q)	\( \sqrt{\frac{3 R T}{M}} \)
(C)	the average kinetic energy of a molecule	(R)	\( \frac{5}{2} R T \)
(D)	the total internal energy of 1 mole of a diatomic gas	(S)	\(\frac32k_BT\)

 

	(A)	(B)	(C)	(D)
1.	(Q)	(P)	(S)	(R)
2.	(R)	(Q)	(P)	(S)
3.	(R)	(P)	(S)	(Q)
4.	(Q)	(R)	(S)	(P)

A cylinder of fixed capacity \(44.8\) litres contains helium gas at standard temperature and pressure. What is the amount of heat needed to raise the temperature of the gas in the cylinder by \(15.0^\circ~\mathrm{C}?\) (\(R=8.31\) J mol^–1 K^–1)

Which of the following parameters is the same for molecules of all gases at a given temperature?

The process on an ideal gas as shown in the figure given below is:
             

1. isothermal
2. isobaric
3. isochoric
4. none of these

If \(C_p\) and \(C_v\) denote the specific heats (per unit mass) of an ideal gas of molecular weight \(M\) (where \(R\) is the molar gas constant), the correct relation is:
1. \(C_p-C_v=R\)
2. \(C_p-C_v=\frac{R}{M}\)
3. \(C_p-C_v=MR\)
4. \(C_p-C_v=\frac{R}{M^2}\)

Hydrogen gas is contained in a vessel and the RMS speed of the gas molecules is \(v\). The gas is heated isobarically so that its volume doubles, then it is compressed isothermally so that it returns to the same volume. The final RMS speed of the molecules will be:

The pressure exerted by a gas enclosed within a room is due to:

An ideal gas equation can be written as $\mathrm{P}=\frac{\mathrm{\rho RT}}{{\mathrm{M}}_0}$ where $\mathrm{\rho }$ and ${\mathrm{M}}_0$ are respectively: