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

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A horizontal uniform glass tube of 100 cm, length sealed at both ends contain 10 cm mercury column in the middle. The temperature and pressure of air on either side of mercury column are respectively 81°C and 76 cm of mercury. If the air column at one end is kept at 0°C and the other end at 273°C, the pressure of air which is at 0°C is (in cm of Hg)

1.  76

2.  68.2

3.  102.4

4.  122

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At standard temperature and pressure the density of a gas is  and the speed of the sound in gas is 330 m/sec. Then the degree of freedom of the gas will be

1.  3

2.  4

3.  5

4.  6

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The temperature of 5 moles of a gas which was held at constant volume was changed from $100°\mathrm{C}$ to $120°\mathrm{C}$. The change in internal energy was found to be 80 Joules. The total heat capacity of the gas at constant volume will be equal to

1.  8 J/K

2.  0.8 J/K

3.  4.0 J/K

4.  0.4 J/K

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The temperature at which the r.m.s. speed of hydrogen molecules is equal to escape velocity on earth surface, will be

1.  1060 K

2.  5030 K

3.  8270 K

4.  10063 K

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Inside a cylinder having insulating walls and closed at ends is a movable piston, which divides the cylinder into two compartments. On one side of the piston is a mass m of a gas and on the other side a mass 2 m of the same gas. What fraction of volume of the cylinder will be occupied by the larger mass of the gas when the piston is in equilibrium ? Consider that the movable piston is conducting so that the temperature is the same throughout

1.  $\frac{1}{4}$

2.  $\frac{1}{3}$

3.  $\frac{1}{2}$

4.  $\frac{2}{3}$

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The diameter of oxygen molecules is  The Vander Waal's gas constant 'b' in ${\mathrm{m}}^{3}/\mathrm{mol}$ will be

1.  $3.2$

2.  $16$

3.  $32×{10}^{-4}$

4.  $32×{10}^{-6}$

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The temperature of the mixture of one mole of helium and one mole of hydrogen is increased from $0°\mathrm{C}$ to $100°\mathrm{C}$ at constant pressure. The amount of heat delivered will be

1.  600 cal

2.  1200 cal

3.  1800 cal

4.  3600 cal

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A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300 K. The ratio of the average rotational kinetic energy per ${\mathrm{O}}_{2}$ molecule to that per ${\mathrm{N}}_{2}$ molecule is

1.  1 : 1

2.  1 : 2

3.  2 : 1

4.  Depends on the moments of inertia of the two molecules

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A vessel contains 14 gm (7 moles) of hydrogen and 96 gm (3 moles) of oxygen at STP. A chemical reaction is induced by passing electric spark in the vessel till one of the gases is consumed. The temperature is brought back to it's starting value 273 K. The pressure in the vessel is

1.  0.1 atm

2.  0.2 atm

3.  0.3 atm

4.  0.4 atm