Question 1: Palette 1/21

JEE Advanced 2024 MCQ

A closed vessel contains $10 \mathrm{~g}$ of an ideal gas $\mathbf{X}$ at $300 \mathrm{~K}$, which exerts $2 \mathrm{~atm}$ pressure. At the same temperature, $80 \mathrm{~g}$ of another ideal gas $\mathbf{Y}$ is added to it and the pressure becomes $6 \mathrm{~atm}$. The ratio of root mean square velocities of $\mathbf{X}$ and $\mathbf{Y}$ at $300 \mathrm{~K}$ is

A

$2 \sqrt{2}: \sqrt{3}$

B

$2 \sqrt{2}: 1$

C

$1: 2$

D

$2: 1$

Question 2: Palette 2/21

JEE Advanced 2020 MCQ

If the distribution of molecular speeds of a gas is as per the figure shown below, then the ratio of the most probable, the average, and the root mean square speeds, respectively, is

A

1 : 1 : 1

B

1 : 1 : 1.224

C

1 : 1.128 : 1.224

D

1 : 1.128 : 1

Question 3: Palette 3/21

JEE Advanced 2015 MCQ

One mole of a monoatomic real gas satisfies the equation p(V $-$ b) = RT where b is a constant. The relationship of interatomic potential V(r) and interatomic distance r for the gas is given by

A

B

C

D

Question 4: Palette 4/21

JEE Advanced 2014 MSQ

An ideal gas in thermally insulated vessel at internal pressure = p₁, volume = V₁ and absolute temperature = T₁ expands irreversibly against zero external pressure, as shown in the diagram.

The final internal pressure, volume and absolute temperature of the gas are p₂, V₂ and T₂, respectively. For this expansion

A

q = 0

B

T₂ = T₁

C

p₂V₂ = p₁V₁

D

p₂V$_2^\gamma $ = p₁$_1^\gamma $

Question 5: Palette 5/21

JEE Advanced 2012 MCQ

For one mole of a van der Waals gas when b = 0 and T = 300 K, the PV vs. 1/V plot is shown below. The value of the van der Waals constant a (atm L² mol^$-$2) is

A

1.0

B

4.5

C

1.5

D

3.0

Question 6: Palette 6/21

JEE Advanced 2011 MSQ

According to kinetic theory of gases

A

collisions are always elastic

B

heavier molecules transfer more momentum to the wall of the container

C

only a small number molecules have very high velocity

D

between collisions, the molecules move in straight line with constant velocity

Question 7: Palette 7/21

JEE Advanced 2009 MCQ

The term that corrects for the attractive forces present in a real gas in the van der Waals equation is

A

$nb$

B

${{a{n^2}} \over {{V^2}}}$

C

$ - {{a{n^2}} \over {{V^2}}}$

D

$ - nb$

Question 8: Palette 8/21

JEE Advanced 2008 MSQ

A gas described by van Der Waals equation

A

behaves similar to an ideal gas in the limit of large molar volumes.

B

behaves similar to an ideal gas in the limit of large pressures.

C

is characterized by van der Waals coefficients that are dependent on the identity of the gas but are independent of the temperature.

D

has the pressure that is lower than the pressure exerted by the same gas behaving ideally.

Question 9: Palette 9/21

JEE Advanced 2007 MCQ

Match gases under specified conditions listed in Column I with their properties/laws in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 $\times$ 4 matrix given in the ORS.

	Column I		Column II
(A)	hydrogen gas (P = 200 atm, T = 273 K)	(P)	Compressibility factor $\ne$ 1
(B)	hydrogen gas (P $\sim$ 0, T = 273 K)	(Q)	attractive forces are dominant
(C)	CO$_2$ (P = 1 atm, T = 273 K)	(R)	PV = nRT
(D)	real gas with very large molar volume	(S)	$P(V-nb)=nRT$

A

A - (s); B - (r); C - (q); D - (p, s)

B

A - (p, s); B - (r, q); C - (p, q); D - (s)

C

A - (p); B - (r); C - (p, q); D - (s)

D

A - (p, s); B - (r); C - (p, q); D - (p, s)

Question 10: Palette 10/21

JEE Advanced 2006 MCQ

The given graph represents the variation of Z (compressibility factor $=\mathrm{PV} / n \mathrm{RT}$ ) versus P , for three real gases $\mathrm{A}, \mathrm{B}$ and C . Identify the only incorrect statement.

A

For the gas A, $a=0$ and its dependence on P is linear at all pressure.

B

For the gas $\mathrm{B}, b=0$ and its dependence on P is linear at all pressure.

C

For the gas C , which is typical real gas for which neither $a=0$ nor $b=0$. By knowing the minima and the point of intersection, with $Z=1, a$ and $b$ can be calculated.

D

At high pressure, the slope is positive for all real gases.

Question 11: Palette 11/21

JEE Advanced 1996 MCQ

A mixture of ideal gas is cooled upto liquid helium temperature (4.22K) to form an ideal solution

A

TRUE

B

FALSE

Question 12: Palette 12/21

JEE Advanced 1993 MCQ

In the van der Waal's equation (P + ${{{n^2}a} \over {{V^2}}}$)(V - nb) = nRT the constant 'a' reflects the actual volume of the gas molecules.

A

TRUE

B

FALSE

Question 13: Palette 13/21

JEE Advanced 1986 MCQ

The average velocity of an ideal gas molecule at 27^oC is 0.3m/sec. The average velocity at 927^oC will be

A

0.6 m/sec

B

0.3 m/sec

C

0.9 m/sec

D

3.0 m/sec

Question 14: Palette 14/21

JEE Advanced 1985 MCQ

Rate of diffusion of a gas is

A

directly proportional to its density

B

directly proportional to the square root of its molecular weight

C

inversely proportional to the square root of its molecular weight.

D

directly proportional to its molecular weight

Question 15: Palette 15/21

JEE Advanced 1985 MCQ

Kinetic Energy of a Molecule is zero at 0^oC.

A

TRUE

B

FALSE

Question 16: Palette 16/21

JEE Advanced 1985 MCQ

A gas in a closed container will exert much higher pressure due to gravity at the bottom than at the top.

A

TRUE

B

FALSE

Question 17: Palette 17/21

JEE Advanced 1984 MCQ

Equal weights of methane and hydrogen are mixed in an empty container at 25^oC. The fraction of the total pressure exerted by hydrogen is

A

1/2

B

8/9

C

1/9

D

16/17

Question 18: Palette 18/21

JEE Advanced 1982 MCQ

Helium atom is two times heavier than a hydrogen molecule. At 298 K, the average kinetic energy of a helium atom is

A

two times that of a hydrogen molecule

B

four times that of a hydrogen molecule

C

same as that of a hydrogen molecule

D

half that of a hydrogen molecule

Question 19: Palette 19/21

JEE Advanced 1981 MCQ

The temperature at which a real gas obeys the ideal gas aws over a wide range of pressure is

A

Critical temperature

B

Boyle temperature

C

Inversion temperature

D

Reduced temperature

Question 20: Palette 20/21

JEE Advanced 1981 MCQ

The ratio of root mean square velocity to average velocity of a gas molecule at a particular temperature is

A

1.086:1

B

1:1.086

C

2:1.086

D

1.086:2

Question 21: Palette 21/21

JEE Advanced 1981 MCQ

Equal weights of methane and oxygen are mixed in an empty container at 25^oC. The fraction of the total pressure exerted by oxygen is

A

1/3

B

1/2

C

2/3

D

${1 \over 3} \times {{273} \over {298}}$