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QUESTION: 1

An ideal gas is expanded adiabatically. How many times the gas to be expanded to reduce the rms velocity of molecules 2 times.

Select one:

Solution:

To reduce the rms velocity two times, temperature should be reduced by 4 times.

∴

V_{1} = V, V_{2} = ?

From adiabatic law,

⇒

⇒

⇒

⇒

The correct answer is: 16 times

QUESTION: 2

A box containing N molecules of a perfect gas at temperature T_{1} and pressure p_{1}.

The number of molecules in the box is doubled keeping the total kinetic energy of the gas same as before. If the new pressure is p_{2} and temperature T_{2}, then.

Select one:

Solution:

Kinetic energy of N molecule of gas

Initially and finally

But E_{1}= E_{2} and N_{2} = 2N_{1}

⇒

⇒

Since the kinetic energy is constant

⇒

⇒ N_{1} T_{1} = N_{2} T_{2}

⇒ NT = constant

and pV = NkT

⇒ p_{1} V_{1} = p_{2} V_{2}

∴ p_{1} = p_{2} (as V_{1} = V_{2} )

The correct answer is:

QUESTION: 3

Three closed vessels A, B and C are at the same temperature T and contain gases which obey Maxwellian distribution of velocities. Vessel A contains only O_{2} , B only N_{2} and C a mixture of equal quantities of O_{2} and N_{2}. If the average speed of O_{2} molecules is vessel A is v_{1} , that of the N_{2} molecules in vessel R is v_{2} , the average speed of O_{2} molecule in vessel C is (where M is the mass of an oxygen molecule)

Select one:

Solution:

Average speed of gas molecules

It depends on temperature and molecular mass so the average speed of oxygen will be same in vessel C and A and that is equal to v_{1}.

The correct answer is: v_{1}

QUESTION: 4

Gas at pressure p_{0} contained in a vessel. If the masses of all the molecules are halved and their speeds are doubled, the resulting pressure p will be equal to.

Select one:

Solution:

⇒

⇒

⇒ p_{2} = 2p_{1} = 2p_{0}

The correct answer is:

QUESTION: 5

Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecule inside will.

Select one:

Solution:

If a lorry is moving with constant velocity than the v_{rms} of gas molecules inside the container will not along and we know that T ∝ v_{rms} so temperature remains same.

The correct answer is: Remain same

QUESTION: 6

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

Select one:

Solution:

Mean kinetic energy of the molecule

where

T = temperature in Kelvin and

t = temperature in Celsius

⇒ Boltzmann constant

Comparing with y = mx + c

⇒ Graph between E and t will be a straight line with positive intercept on E-axisand positive slope with t-axis.

The correct answer is:

QUESTION: 7

At what temperature is the root mean square velocity of gaseous hydrogen molecules is equal to that of the oxygen molecules at 47°C.

Select one:

Solution:

For oxygen O_{2},

and for hydrogen H_{2},

According to problem,

⇒

⇒

The correct answer is: 20 K

QUESTION: 8

An air bubble of volume V_{0} is released by a fish at a depth h in a lake. The bubble rises to the surface. Assume constant temperature and standard atmosphere pressure P above the lake. The volume of the bubble just before touching the surface will be (density of water is ρ.

Select one:

Solution:

According to Boyle’s law, multiplication of pressure and volume will remain constant at bottom and top.

If p is atmospheric pressure at the top of the lake and the volume of bubble is V then

p_{1}V_{1} = p_{2} V_{2}

⇒ (p + hρp)V_{0} = pV

⇒

The correct answer is:

QUESTION: 9

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

Select one:

Solution:

When temperature of gas increases, it expands. As the cross-sectional area of right piston is more, therefore greater force will work on it (F = PA). So piston will move towards right.

The correct answer is: Move towards right

QUESTION: 10

The figure below shows graph of pressure and volume of a gas at two temperatures T_{1} and T_{2} which of the following inferences is correct?

Select one:

Solution:

For a given pressure, volume will be more if temperature is more (Charle’s law) From the graph, it is clear that V_{2} > V_{1}

∴ T_{2} > T_{1}

The correct answer is:

T_{1}< T_{2}

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