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*Multiple options can be correct

QUESTION: 1

A gas in container A is in thermal equilibrium with another gas in container B, both contain equal masses of two gases in the respective containers which of the following can be true?

Select one or more:

Solution:

According to the problem, mass of gases are equal so number of moles will not be equal i.e.

From ideal gas equations :

∴

(∴ temperature of container are equal)

From this relation, it is clear that if p_{A} = p_{B} then

Similarly if V_{A} = V_{B} then i.e. p_{A} ≠ p_{B.}

The correct answers are:

*Multiple options can be correct

QUESTION: 2

Let and v_{mp} respectively denote mean speed, root mean square speed and most probable speed of the molecules in an ideal monoatomic gas at absolute temperature T. The mass of molecule is m. Then,

Select one or more:

Solution:

We know that

so,

∴ Average kinetic energy

The correct answers are: The average kinetic energy of a molecule is

*Multiple options can be correct

QUESTION: 3

Under which of the following conditions is the law pV = RT obeyed most closely by a real gas

Select one or more:

Solution:

At low pressure and high temperature real gas obey pV = RT i.e. they behave as ideal gas because at high temperature we can assume that there is no force of attraction or repulsion works among the molecules and the volume occupied by the molecules is negligible in comparison to the volume occupied by the gas.

The correct answers are: Low pressure, High temperature

*Multiple options can be correct

QUESTION: 4

A gas mixture consists of molecules of type 1, 2 and 3 with molar masses m_{1} > m_{2} > m_{3} . v_{rms} and are the rms speed and average kinetic energy of the gases. Which of the following are true?

Select one or more:

Solution:

The rms speed depends upon the molecular mass. but kinetic energy does not depend on it.

i.e.

On the problem

∴

But

The correct answers are:

*Multiple options can be correct

QUESTION: 5

Which of the following statements are true with regards to mean free path?

Select one or more:

Solution:

As i.e. mean free path is inversely proportional to density of a gas. As

For constant volume and thus constant number density n of gas molecule. P/T is constant so, λ will not depend on p and T.

But if volume of given mass of a gas is allowed to change with p and T, then at constant pressure and at constant temperature.

The correct answers are: Mean free path is inversely proportional to density of gas, For constant volume, will not depend on T and p

*Multiple options can be correct

QUESTION: 6

Read the given statements and choose which is/are incorrect on the basis of kinetic theory of gases.

Select one or more:

Solution:

If the gas is not ideal then its molecule will posses potential energy. Hence statement (a) is wrong. rms speed of different gases at some temperature depends on its molecules weight Hence, statement (b) is wrong.

Kinetic energy of one gram gas depends on the molecular weight . Hence, statement (c) is wrong.

But kinetic energy of one mole of ideal gas does not depend on the molecular weight Hence (d) is correct.

The correct answers are: Energy of one molecule at absolute to temperature is zero, rms speeds of different gas are same at same temperature, For one gram of all ideal gas, Kinetic energy is same at same temperature.

*Multiple options can be correct

QUESTION: 7

The value of C_{P} – C_{V} = R for a gas in state A and C_{P} – C_{V} = 1.06R in another state B. If p_{A} and p_{B} denote the pressure and T_{A} and T_{B} denote the temperature in the two state, then

Select one or more:

Solution:

For state A, C_{p} - C_{V} = R i.e. gas behaves as ideal gas. For state B, C_{p} – C_{v} = 1.06R ≠ R i.e. gas does not behave like ideal gas, and we know that at high temperature and at low pressure nature of gas may be ideal so we can say that p_{A} < p_{B} and T_{A} > T_{B} .

The correct answers are: p_{A} < p_{B} , T_{A} > T_{B}

*Multiple options can be correct

QUESTION: 8

Two identical containers each of volume V_{0} are joined by a small pipe. The containers contains identical gases at temperature T_{0} and pressure p_{0} . One container is heated to temperature 2T_{0} while maintaining the other at same temperature. The common pressure of gas is p and n is the number of the moles of gas in container at temperature 2T_{0} .

Select one or more:

Solution:

Initially for container A,

For container B, p_{0} V_{0} = n_{0} RT_{0}

∴

Total number of moles = n_{0} + n_{0} = 2n_{0}

Since even on heating, total number of moles is conserved, hence

n_{1} + n_{2} = 2n_{0} .....(1)

If p be the common pressure, then for container A,

pV_{0} = n_{1} R2T_{0}

⇒

For container B,

⇒

Substituting the value of n_{0} , n_{1} and n_{2} is equation (1), we get

⇒

Number of mole in container A (at temperature 2T_{0} )

The correct answers are:

*Multiple options can be correct

QUESTION: 9

The equation of state of a gas is given by where a, b, c, and R are constants. The isotherms can be represented by p = AV^{m} – BV^{n} where A and B depends only on temperature then.

Select one or more:

Solution:

⇒

⇒

Compairing thus with p = AV^{m} – BV^{n}

we get m = –c and n = –1.

The correct answers are:

m = -c,

n = –1

*Multiple options can be correct

QUESTION: 10

Which of the following is/are false?

Select one or more:

Solution:

At absolute temperature, kinetic energy of gas molecules becomes zero but they possess potential energy so we can say that at absolute zero degree temperature is not zero energy temperature.

The correct answers are: Two different gases at the same temperature and pressure have equal root mean square velocities, The rms speed of the molecules of different ideal gases, maintained at some temperature are the same, Given sample of ice of hydrogen and ice of oxygen both at NTP oxygen sample has a large number of molecules

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