Two containers of equal volumes contain the same gas at pressures \(P_1\)${\mathrm{}}_{}$ and \(P_2\) and absolute temperatures \(T_1\) and \(T_2\), respectively. On joining the vessels, the gas reaches a common pressure \(P\) and common temperature \(T\). The ratio \(\dfrac{P}{T}\) is equal to:

1.	\(\dfrac{P_1}{T_1}+\dfrac{P_2}{T_2}\)	2.	\(\dfrac{P_1T_1+P_2T_2}{(T_1+T_2)^2}\)
3.	\(\dfrac{P_1T_2+P_2T_1}{(T_1+T_2)^2}\)	4.	\(\dfrac{P_1}{2T_1}+\dfrac{P_2}{2T_2}\)

At the top of a mountain, a thermometer reads \(7^\circ \text{C}\) and a barometer reads \(70\) cm of mercury. At the bottom of the mountain, the thermometer reads \(27^\circ \text{C},\) and the barometer reads \(76\) cm of mercury.

What is the comparison (ratio) of the air density at the top of the mountain to that at the bottom?

A vessel is partitioned in two equal halves by a fixed diathermic separator. Two different ideal gases are filled in left (L) and right (R) halves. The rms speed of the molecules in L part is equal to the mean speed of molecules in the R part. Then the ratio of the mass of a molecule in L part to that of a molecule in R part is

1. $\sqrt{\frac{3}{2}}$                           

2. $\sqrt{\frac{\mathrm{\pi }}{4}}$

3. $\sqrt{\frac{2}{3}}$                           

4. $\frac{3\mathrm{\pi }}{8}$

A gas is filled in the cylinder shown in the figure. The two pistons are joined by a string. If the gas is heated, the pistons will

1.Move towards left                 

2. Move towards right

3. Remain stationary                 

4. None of these

A closed vessel contains 8gm of oxygen and 7gm of nitrogen. The total pressure is 10 atm at a given temperature. If now oxygen is absorbed by introducing a suitable absorbent the pressure of the remaining gas in atm will be

1.  2                               

2.  10

3.  4                               

4.  5

${\mathrm{CO}}_2\left(\mathrm{O}=\mathrm{C}=\mathrm{O}\right)$ is a triatomic gas. Mean kinetic energy of one gram gas will be (If N-Avogadro's number, k-Boltzmann's constant and molecular weight of ${\mathrm{CO}}_2=44$ , Degree of freedom f = 7)

1. $\left(3/88\right) \mathrm{NkT}$                             

2. $\left(5/88\right) \mathrm{NkT}$

3. $\left(6/88\right) \mathrm{NkT}$                             

4. $\left(7/88\right) \mathrm{NkT}$

40 calories of heat is needed to raise the temperature of 1 mole of an ideal monoatomic gas from 20°C to 30°C at a constant pressure. The amount of heat required to raise its temperature over the same interval at a constant volume $\left(\mathrm{R}=2 \mathrm{calorie} {\mathrm{mole}}^{-1} {\mathrm{K}}^{-1}\right)$ is

1.  20 calorie                   

2.  40 calorie

3.  60 calorie                   

4.  80 calorie

The pressure and volume of saturated water vapour are P and V respectively. It is compressed isothermally thereby volume becomes V/2, the final pressure will be

1.  More than 2P                         

2.  P

3.  2P                                         

4.  4P

If the intermolecular forces vanish away, the volume occupied by the molecules contained in 4.5 kg water at standard temperature and pressure will be

1.  $5.6 {\mathrm{m}}^3$                             

2.  $4.5 {\mathrm{m}}^3$

3.  $11.2 \mathrm{litre}$                           

4.  $11.2 {\mathrm{m}}^3$

When an air bubble of radius ‘r’ rises from the bottom to the surface of a lake, its radius becomes 5r/4 (the pressure of the atmosphere is equal to the 10 m height of water column). If the temperature is constant and the surface tension is neglected, the depth of the lake is

1.  3.53 m                   

2.  6.53 m

3.  9.53 m                   

4.  12.53 m