An isolated system-

The pressure and temperature of two different gases are P and T with volume V for each.  If they are mixed, keeping the same volume and temperature, the pressure of the mixture will be:
1. P/2        

2. P             

3. 2P           

4. 4P

If the mean free path of atoms is doubled then the pressure of the gas will become:
1. \(P/4\)           
2. \(P/2\)           
3. \(P/8\)           
4. \(P\)

A diatomic molecule has how many degrees of freedom-                                                                                             

(1) 3            (2) 4           (3) 5              (4) 6

A thermally insulated piston divides a container into two compartments.  Volume, temperature, and pressure in the right compartment are 2V, T and 2P, while in the left compartment the respective values are V, T and P.  If the piston can slide freely, then in the final equilibrium position, the volume of the right-hand compartment will be :
1. V
2. $\frac{3V}{5}$
3. $\frac{9V}{4}$
4. $\frac{12V}{5}$

The graph which represents the variation of mean kinetic energy of molecules with temperature $t°C$ is ?

(1)

(2)

(3) 

(4)

$V_{rms},V_{av},V_{mp}$ are root mean square, average and most probable speeds of molecules of a gas obeying Maxwellian velocity distribution. Which of the following statements is correct?

1. $V_{rms}<V_{av}<V_{mp}$

2. $V_{rms}>V_{av}>V_{mp}$

3. $V_{rms} < V_{av}>V_{mp}$

4. $V_{avg}>V_{rms}<V_{mp}$

Gas is found to obey the law $P^{2}V$ = constant. The initial temperature and volume are $T_0$ and $V_0$. If the gas expands to a volume $3V_0$, its final temperature becomes:

1. $\frac{T_0}{3}$           

2. $\frac{T_0}{\sqrt{3}}$

3. $3T_0$           

4. None of these

For a gas, the r.m.s speed at 800 K is:

1. Four times the value at 200 K

2. Half the value at 200 K

3. Twice the value at 200 K

4. Same as at 200 K

The average kinetic energy of a helium atom at $30°C$ is:                                                                                           [MP PMT 2004]

1. Less than 1 eV

2. A few KeV

3. 50-60 eV

4. 13.6 eV