An isolated system-

(A) is a specified region where transfers of energy and mass take place

(B) is a region of constant mass and only energy is allowed to close the boundaries

(C) is one in which mass within the system is not necessarily constant.

(D) cannot transfer either energy of mass to or from the surroundings.

The pressure and temperature of two different gases are P and T having the volume V for each.  They are mixed keeping the same volume and temperature, the pressure of the mixture will be-                                                          [Pb. PMT 1997, 98; DPMT 1999; MH CET 2003]

(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:                                                                           [RPMT 2000]

(1) P/4            (2) P/2           (3) P/8           (4) P

A diatomic molecule has how many degrees of freedom-                                                                                              [Pb. PET 2000]

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

A gas mixture consists of 2 moles of $O_2$ and 4 moles of $Ar$ at temperature T.  Neglecting all vibrational modes, the total internal energy of the system is-

(1) 4 RT             (2) 15 RT          (3) 9 RT              (4) 11 RT 

Which of the following relations is correct for the root-mean-square speed of gas at temperature T?

Where, k= Boltzmann constant, and m= mass of a molecule.

(A) $V_{r.m.s}=\sqrt{\frac{3 k\hspace{0.17em}T}{m}}$    (B)$V_{r.m.s}=\sqrt{\frac{8 k\hspace{0.17em}T}{m \mathrm{\pi }}}$

(C) $V_{r.m.s}=\sqrt{\frac{2 k\hspace{0.17em}T}{m}}$    (D) $V_{r.m.s}=\sqrt{\frac{m}{3 k T}}$

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)

Gas at pressure $P_0$ is contained in a vessel.  If the masses of all the molecules are halved and their speeds doubled, the resulting pressure p will be equal to:

(1) 4 $P_0$           (2) 2 $P_0$          (3) $P_0$       (4) $\frac{P_2}{2}$

$V_{rms},V_{av},V_{mp}$ 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. $V_{avg}>V_{rms}<V_{mp}$