$$\begin{gathered} At what temperature, is the root mean square speed \\ of molecules of hydrogen is twice of that at STP? \\ \left(A\right) 273 K \\ \left(B\right) 546 K \\ \left(C\right) 819 K \\ \left(D\right) 1092 K \end{gathered}$$

At what temperature, is the root mean square velocity of gaseous hydrogen molecules equal to that of oxygen molecules at 47$°$C:[MP PET 1997, 2000; RPET 1999; AIEEE 2002; J & K CET 2004; Kerala PET 2010]

(1) 20 K           (2) 80 K           (3) - 73 K              (4) 3 K

The average kinetic energy of a gas molecule can be determined by knowing:                                        [RPET 2000, MP PET 2010]

(1) The number of molecules in the gas

(2) The pressure of the gas only

(3) The temperature of the gas only

(4) None  of the above is enough by itself

 Volume, pressure, and temperature of an ideal gas are V, P, and T respectively. If the mass of its molecule is m, then its density is [k=boltzmann's constant]

(a) mkT                              (b) $\frac{P}{kT}$

(d)$\frac{P}{kTV}$                             (d) $\frac{Pm}{kT}$

One litre of gas A and two litres of gas B, both having the same temperature 100$°$C and the same pressure 2.5 bar will have the ratio of kinetic energies of their molecules as:

(1) 1:1       (2) 1:2       (3) 1:4         (4) 4:1

On 0$°$C, the pressure measured by the barometer is 760 mm.  What will be pressure at 100$°$C?                                  [AFMC 2002]

(1) 760 mm        (2) 730 mm          (3) 780 mm           (4) None of these

By what percentage, should the pressure of a given mass of gas be increased, so as to decrease its volume by 10% at a constant temperature?

(1) 5%      (2) 7.2 %         (3) 12.5%          (4) 11.1%

In the adjacent V-T diagram what is the relation between $P_1 and P_2$ ?

(a) $P_2=P_1$                         (b) $P_2>P_1$

(c) $P_2<P_1$                         (d) Cannot be predicated

The ratio $\frac{C_p}{C_V}=\gamma$ for a gas.  Its molecular weight is M. Its specification heat capacity at constant pressure is 

(1) $\frac{R}{\gamma -1}$                (2) $\frac{\gamma R}{\gamma -1}$

(3) $\frac{\gamma R}{M(\gamma -1)}$         (4) $\frac{\gamma RM}{(\gamma -1)}$

Which one of the following graph is correct at constant pressure

1.              2.  

3.               4.