Kinetic Theory of Gases

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JEE Main 2021

A cylindrical container of volume $4.0 \times 1 0^{- 3} m^{3}$ contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is $400 K$ . The pressure of the mixture of gases is [Take, gas constant $= 8.3 J mol^{- 1} K^{- 1}$ ]

249 \times 1 0^{1} Pa

(B)

24.9 \times 1 0^{3} Pa

(C)

24.9 \times 1 0^{5} Pa

(D)

24.9 Pa

JEE Main 2019

LEVELJEE Main

A mixture of 2 moles of helium gas (atomic mass = 4u) and 1 mole of argon gas (atomic mass = 40u) is kept at 300 K in a container. The ratio of their rms speeds $[\frac{v _{rms(helium)}}{v _{rms(argon)}}]$ is close to

Consider a sample of oxygen behaving like an ideal gas. At $300 K$ , the ratio of root mean square (rms) velocity to the average velocity of gas molecule would be (Molecular weight of oxygen is $32 g/mol$ ; $R = 8.3 J K^{- 1} mol^{- 1}$ )

(A)

\frac{3}{8}

(B)

\frac{8}{3}

(C)

\frac{3 π}{8}

(D)

\frac{8 π}{3}

JEE Main 2019

LEVELJEE Main

If $1 0^{22}$ gas molecules each of mass $1 0^{- 26}$ kg collide with a surface (perpendicular to it) elastically per second over an area $1 m^{2}$ with a speed $1 0^{4}$ m/s, the pressure exerted by the gas molecules will be of the order of

(A)

1 0^{4} N/m^{2}

(B)

1 0^{8} N/m^{2}

(C)

1 0^{3} N/m^{2}

(D)

1 0^{16} N/m^{2}

JEE Main 2021

LEVELBoard

Consider a mixture of gas molecule of types $A$ , $B$ and $C$ having masses $m_{A} < m_{B} < m_{C}$ . The ratio of their root mean square speeds at normal temperature and pressure is

(A)

v_{A} = v_{B} = v_{C} = 0

(B)

\frac{1}{v _{A}} > \frac{1}{v _{B}} > \frac{1}{v _{C}}

(C)

v_{A} = v_{B} \neq = v_{C}

(D)

\frac{1}{v _{A}} < \frac{1}{v _{B}} < \frac{1}{v _{C}}

LEVELJEE Main

Three perfect gases at absolute temperatures $T_{1}, T_{2}$ and $T_{3}$ are mixed. The masses of molecules are $m_{1}, m_{2}$ and $m_{3}$ and the number of molecules are $n_{1}, n_{2}$ and $n_{3}$ respectively. Assuming no loss of energy, the final temperature of the mixture is

(A)

\frac{n _{1} T _{1} + n _{2} T _{2} + n _{3} T _{3}}{n _{1} + n _{2} + n _{3}}

(B)

\frac{n _{1} T _{1}^{2} + n _{2} T _{2}^{2} + n _{3} T _{3}^{2}}{n _{1} T _{1} + n _{2} T _{2} + n _{3} T _{3}}

(C)

\frac{n _{1}^{2} T _{1} + n _{2}^{2} T _{2} + n _{3}^{2} T _{3}}{n _{1} T _{1} + n _{2} T _{2} + n _{3} T _{3}}

(D)

\frac{( T _{1} + T _{2} + T _{3} )}{3}

JEE Main 2021

LEVELJEE Main

Two ideal polyatomic gases at temperatures $T_{1}$ and $T_{2}$ are mixed so that there is no loss of energy. If $f_{1}$ and $f_{2}$ , $m_{1}$ and $m_{2}$ , $n_{1}$ and $n_{2}$ be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is

(A)

\frac{n _{1} T _{1} + n _{2} T _{2}}{n _{1} + n _{2}}

(B)

\frac{n _{1} f _{1} T _{1} + n _{2} f _{2} T _{2}}{n _{1} f _{1} + n _{2} f _{2}}

(C)

\frac{n _{1} f _{1} T _{1} + n _{2} f _{2} T _{2}}{f _{1} + f _{2}}

(D)

\frac{n _{1} f _{1} T _{1} + n _{2} f _{2} T _{2}}{n _{1} + n _{2}}

JEE Main 2020

LEVELJEE Advanced

Two gases-argon (atomic radius 0.07 nm, atomic weight 40) and xenon (atomic radius 0.1 nm, atomic weight 140) have the same number density and are at the same temperature. The ratio of their respective mean free times is closest to

A container is divided into two chambers by a partition. The volume of first chamber is $4.5$ L and second chamber is $5.5$ L. The first chamber contain $3.0$ mol of gas at pressure $2.0$ atm and second chamber contain $4.0$ mol of gas at pressure $3.0$ atm. After the partition is removed and the mixture attains equilibrium, then the common equilibrium pressure existing in the mixture is $x \times 1 0^{- 1}$ atm. Value of $x$ is ......... .

JEE Main 2019

LEVELJEE Main

A vertical closed cylinder is separated into two parts by a frictionless piston of mass $m$ and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is $l_{1}$ and that below the piston is $l_{2}$ , such that $l_{1} > l_{2}$ . Each part of the cylinder contains $n$ moles of an ideal gas at equal temperature $T$ . If the piston is stationary, its mass $m$ , will be given by (where, $R$ is universal gas constant and $g$ is the acceleration due to gravity)

(A)

\frac{n R T}{g} [\frac{l _{1} - l _{2}}{l _{1} l _{2}}]

(B)

\frac{n R T}{g} [\frac{1}{l _{2}} + \frac{1}{l _{1}}]

(C)

\frac{R T}{g} [\frac{2 l _{1} + l _{2}}{l _{1} l _{2}}]

(D)

\frac{R T}{n g} [\frac{l _{1} - 3 l _{2}}{l _{1} l _{2}}]

JEE Main 2020

LEVELJEE Advanced

Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently, the mean collision time between the gas molecule changes from $τ_{1}$ to $τ_{2}$ . If $\frac{C _{p}}{C _{V}} = γ$ for this gas, then a good estimate for $\frac{τ _{1}}{τ _{2}}$ is given by

(A)

(\frac{1}{2})^{\frac{γ + 1}{2}}

(B)

\frac{1}{2}

(C)

2

(D)

(\frac{1}{2})^{γ}

JEE Main 2021

LEVELJEE Main

For a gas $C_{p} - C_{V} = R$ in a state $P$ and $C_{p} - C_{V} = 1.10 R$ in a state $Q$ . $T_{P}$ and $T_{Q}$ are the temperatures in two different states $P$ and $Q$ , respectively. Then,

(A)

T_{P} = T_{Q}

(B)

T_{P} < T_{Q}

(C)

T_{P} = 0.9 T_{Q}

(D)

T_{P} > T_{Q}

JEE Main 2021

LEVELJEE Main

If the rms speed of oxygen molecules at $0^{\circ} C$ is $160 m/s$ , find the rms speed of hydrogen molecules at $0^{\circ} C$ .

The volume $V$ of an enclosure contains a mixture of three gases, $16 g$ of oxygen, $28 g$ of nitrogen and $44 g$ of carbon dioxide at absolute temperature $T$ . Consider $R$ as universal gas constant. The pressure of the mixture of gases is

(A)

\frac{88 R T}{V}

(B)

\frac{3 R T}{V}

(C)

\frac{5}{2} \frac{R T}{V}

(D)

\frac{4 R T}{V}

JEE Main 2020

LEVELJEE Main

Nitrogen gas is at $30 0^{\circ} C$ temperature. The temperature (in K) at which the rms speed of a $H_{2}$ molecule would be equal to the rms speed of a $N_{2}$ molecule is ......... (Molar mass of $N_{2}$ gas is $28 g$ .)

JEE Main 2019

LEVELJEE Main

2 kg of a monoatomic gas is at a pressure of $4 \times 1 0^{4} N/m^{2}$ . The density of the gas is $8 kg/m^{3}$ . What is the order of energy of the gas due to its thermal motion ?

(A)

1 0^{6} J

(B)

1 0^{3} J

(C)

1 0^{4} J

(D)

1 0^{5} J

JEE Main 2021

LEVELJEE Main

The rms speeds of the molecules of hydrogen, oxygen and carbondioxide at the same temperature are $v_{H}$ , $v_{O}$ and $v_{C O_{2}}$ respectively, then

(A)

v_{H} > v_{O} > v_{C O_{2}}

(B)

v_{C O_{2}} > v_{O} > v_{H}

(C)

v_{H} = v_{O} > v_{C O_{2}}

(D)

v_{H} = v_{O} = v_{C O_{2}}

JEE Main 2021

LEVELJEE Main

On the basis of kinetic theory of gases, the gas exerts pressure because its molecules

(A)

continuously lose their energy till it reaches wall

(B)

are attracted by the walls of container

(C)

continuously stick to the walls of container

(D)

suffer change in momentum when impinge on the walls of container

JEE Main 2021

LEVELJEE Main

A mixture of hydrogen and oxygen has volume $500 cm^{3}$ , temperature $300 K$ , pressure $400 kPa$ and mass $0.76 g$ . The ratio of masses of oxygen to hydrogen will be

Two moles of an ideal gas with $\frac{C _{p}}{C _{V}} = \frac{5}{3}$ are mixed with 3 mol of another ideal gas with $\frac{C _{p}}{C _{V}} = \frac{4}{3}$ . The value of $\frac{C _{p}}{C _{V}}$ for the mixture is

A gas mixture consists of $3$ moles of oxygen and $5$ moles of argon at temperature $T$ . Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of $R T$ ) of the mixture is

If one mole of the polyatomic gas is having two vibrational modes and $β$ is the ratio of molar specific heats for polyatomic gas $(β = \frac{C _{p}}{C _{V}})$ , then the value of $β$ is

For a given gas at $1 atm$ pressure, rms speed of the molecules is $200 m/s$ at $12 7^{\circ} C$ . At $2 atm$ pressure and at $22 7^{\circ} C$ , the rms speed of the molecules will be

(A)

1005 m/s

(B)

80 m/s

(C)

100 m/s

(D)

805 m/s

JEE Main 2020

LEVELJEE Main

The plot that depicts the behaviour of the mean free time $τ$ (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature ( $T$ ), qualitatively is (graphs are schematic and not drawn to scale)

The internal energy ( $U$ ), pressure ( $p$ ) and volume ( $V$ ) of an ideal gas are related as $U = 3 p V + 4$ . The gas is

Either monoatomic or diatomic

(D)

monoatomic only

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Consider a mixture of gas molecule of types A, B and C having masses mA​<mB​<mC​. The ratio of their root mean square speeds at normal temperature and pressure is

Two gases-argon (atomic radius 0.07 nm, atomic weight 40) and xenon (atomic radius 0.1 nm, atomic weight 140) have the same number density and are at the same temperature. The ratio of their respective mean free times is closest to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } For a gas Cp​−CV​=R in a state P and Cp​−CV​=1.10R in a state Q. TP​ and TQ​ are the temperatures in two different states P and Q, respectively. Then,

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the rms speed of oxygen molecules at 0∘C is 160 m/s, find the rms speed of hydrogen molecules at 0∘C.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } 2 kg of a monoatomic gas is at a pressure of 4×104 N/m2. The density of the gas is 8 kg/m3. What is the order of energy of the gas due to its thermal motion ?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The rms speeds of the molecules of hydrogen, oxygen and carbondioxide at the same temperature are vH​, vO​ and vCO2​​ respectively, then

On the basis of kinetic theory of gases, the gas exerts pressure because its molecules

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A mixture of hydrogen and oxygen has volume 500 cm3, temperature 300 K, pressure 400 kPa and mass 0.76 g. The ratio of masses of oxygen to hydrogen will be

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Two moles of an ideal gas with CV​Cp​​=35​ are mixed with 3 mol of another ideal gas with CV​Cp​​=34​. The value of CV​Cp​​ for the mixture is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If one mole of the polyatomic gas is having two vibrational modes and β is the ratio of molar specific heats for polyatomic gas (β=CV​Cp​​), then the value of β is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } For a given gas at 1 atm pressure, rms speed of the molecules is 200 m/s at 127∘C. At 2 atm pressure and at 227∘C, the rms speed of the molecules will be

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The internal energy (U), pressure (p) and volume (V) of an ideal gas are related as U=3pV+4. The gas is

Consider a mixture of gas molecule of types $A$ , $B$ and $C$ having masses $m_{A} < m_{B} < m_{C}$ . The ratio of their root mean square speeds at normal temperature and pressure is

For a gas $C_{p} - C_{V} = R$ in a state $P$ and $C_{p} - C_{V} = 1.10 R$ in a state $Q$ . $T_{P}$ and $T_{Q}$ are the temperatures in two different states $P$ and $Q$ , respectively. Then,

If the rms speed of oxygen molecules at $0^{\circ} C$ is $160 m/s$ , find the rms speed of hydrogen molecules at $0^{\circ} C$ .

2 kg of a monoatomic gas is at a pressure of $4 \times 1 0^{4} N/m^{2}$ . The density of the gas is $8 kg/m^{3}$ . What is the order of energy of the gas due to its thermal motion ?

The rms speeds of the molecules of hydrogen, oxygen and carbondioxide at the same temperature are $v_{H}$ , $v_{O}$ and $v_{C O_{2}}$ respectively, then

A mixture of hydrogen and oxygen has volume $500 cm^{3}$ , temperature $300 K$ , pressure $400 kPa$ and mass $0.76 g$ . The ratio of masses of oxygen to hydrogen will be

Two moles of an ideal gas with $\frac{C _{p}}{C _{V}} = \frac{5}{3}$ are mixed with 3 mol of another ideal gas with $\frac{C _{p}}{C _{V}} = \frac{4}{3}$ . The value of $\frac{C _{p}}{C _{V}}$ for the mixture is

If one mole of the polyatomic gas is having two vibrational modes and $β$ is the ratio of molar specific heats for polyatomic gas $(β = \frac{C _{p}}{C _{V}})$ , then the value of $β$ is

For a given gas at $1 atm$ pressure, rms speed of the molecules is $200 m/s$ at $12 7^{\circ} C$ . At $2 atm$ pressure and at $22 7^{\circ} C$ , the rms speed of the molecules will be

The internal energy ( $U$ ), pressure ( $p$ ) and volume ( $V$ ) of an ideal gas are related as $U = 3 p V + 4$ . The gas is