Kinetic Theory of Gases and ldeal Gas | Physics JEE previous year questions with Solutions

Q 11 :

A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature 50 °C. The gas is now heated to double its temperature. The modified pressure is ____ Pa. [2026]

(3730)

$As per NTA$

$V = constant$

$so P \propto T$

$T_{i} = 50 ° C = 323 K$

$T_{f} = 100 ° C = 373 K$

$\Rightarrow \frac{P_{f}}{P_{i}} = \frac{T_{f}}{T_{i}}$

$\Rightarrow \frac{P_{f}}{3.23 kPa} = \frac{373}{323}$

$\Rightarrow P_{f} = 3730 Pa$

$Other Solution:$

$As volume is constant$

$∴$ $P \propto T$

$Since T is doubled (must be in Kelvin),$ $so pressure$ $must be doubled$

$∴$ $P_{f} = 2 P_{i}$

$P_{f} = 2 \times 3.23 = 6.46 kPa$

$P_{f} = 6460 Pa$

Q 12 :

The mean free path of a molecule of diameter $5 \times 10^{- 10} m$ at the temperature $41 ° C$ and pressure $1.38 \times 10^{5} Pa$ is given as ______ m.

(Given $k_{B} = 1.38 \times 10^{- 23} J/K$ ) [2026]

$10 \sqrt{2} \times 10^{- 8}$
$2 \sqrt{2} \times 10^{- 8}$
$2 \times 10^{- 8}$
$2 \sqrt{2} \times 10^{- 10}$

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(2)

$λ = \frac{k_{B} T}{\sqrt{2} π σ^{2} P}$

$= \frac{1.38 \times 10^{- 23} \times (273 + 41) \times 100}{\sqrt{2} \times 3.14 \times {(5 \times 10^{- 10})}^{2} \times 1.38 \times 10^{5}}$

$= 2 \sqrt{2} \times 10^{- 8}$

Q 13 :

An air bubble of volume $2.9 c m^{3}$ rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is 17 $° C$ . The volume of the bubble when it reaches the surface, where the water temperature is 27 $° C$ , is ____ $c m^{3} .$
(g = 10 $m / s^{2}$ , density of water = $10^{3} k g / m^{3}$ , and 1 atm pressure is $10^{5}$ Pa) [2026]

2.0
4.2
3.0
4.5

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(4)

$For an air bubble rising in water, the number of moles remain constant$

$\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}$

$\frac{(P_{atm} + ρ g h) 2.9 {cm}^{3}}{290 K} = \frac{(P_{atm}) V_{2}}{300}$

$V_{2} = 4.5 {cm}^{3}$

Q 14 :

One mole of an ideal gas passes through a process where pressure and volume obey the pressure $P = P_{0} [1 - \frac{1}{2} {(\frac{V_{0}}{V})}^{2}]$ . Here $P_{0}$ and $V_{0}$ are constants. Calculate the change in the temperature of the gas, if its volume changes from $V_{0}$ to $2 V_{0}$ .

$\frac{1}{2} \frac{P_{0} V_{0}}{R}$
$\frac{5}{4} \frac{P_{0} V_{0}}{R}$
$\frac{3}{4} \frac{P_{0} V_{0}}{R}$
$\frac{1}{4} \frac{P_{0} V_{0}}{R}$

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(2)

We have given, $P = P_{0} [1 + \frac{1}{2} {(\frac{V_{0}}{V})}^{2}]$

When $V_{1} = V_{0}$ $\Rightarrow P_{1} = P_{0} [1 - \frac{1}{2}] = \frac{P_{0}}{2}$

When $V_{2} = 2 V_{0}$

$Δ T =$ $| (\frac{1}{n R}) (P_{1} V_{1} - P_{2} V_{2}) |$ $= (\frac{1}{n R})$ $| (\frac{P_{0} V_{0}}{2} - \frac{7 P_{0} V_{0}}{4}) |$ $= \frac{5 P_{0} V_{0}}{4 n R} = \frac{5 P_{0} V_{0}}{4 R}$ $(∵ n = 1)$

Q 15 :

The number density of molecules of a gas depends on their distance $' r'$ from the origin as, $n (r) = n_{0} e^{- α r^{4}}$ . Then the total number of molecules is proportional to:

$n_{0} α^{- 3 / 4}$
$\sqrt{n_{0}} α^{1 / 2}$
$n_{0} α^{1 / 4}$
$n_{0} α^{- 3}$

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(1)

$N = \int ρ (d v) = \int_{0}^{r} n_{0} e^{- a r^{4}} \times 4 π r^{2} d r = 4 π n_{0} \int_{0}^{r} r^{2} (e^{- a r^{4}}) d r \propto n_{0} a^{- 3 / 4}$

Q 16 :

Number of collisions per second of molecules of a gas on the wall of a container per $m^{2}$ will:

Increase if temperature and volume both are doubled.
Increase if temperature and volume both are halved.
Increase if pressure and temperature both are doubled.
Increase if pressure and temperature both are halved.

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4

Select one or more options

(2,3)

$No. of collisions per unit area \propto \frac{1}{time between two collisions \times area}$

$\frac{n}{A} \propto \frac{V_{rms}}{distance b/w walls \times A}$ $V_{rms} \propto \sqrt{T}$ $Distance b/w walls \times A = volume$

$So \frac{n}{A} \propto \frac{T^{1 / 2}}{V}$

$If both T and V are halved, \frac{n}{A} increases.$

Q 17 :

A system consists of two types of gas molecules A and B having same number density $2 \times 10^{25} / m^{3}$ . The diameter of A and B are 10 $Å$ and 5 $Å$ respectively. They suffer collision at room temperature. The ratio of average distance covered by the molecule A to that of B between two successive collisions is ____ $\times 10^{- 2}$ .

(25)

$∴$ $mean free path$ $λ = \frac{1}{\sqrt{2} π d^{2} n}$

$\frac{λ_{1}}{λ_{2}} = \frac{d_{2}^{2} n_{2}}{d_{1}^{2} n_{1}} = {(\frac{5}{10})}^{2} = 0.25 = 25 \times 10^{- 2}$

Q 18 :

STATEMENT-1: Each molecule of a gas moves with rms speed if the temperature of gas is constant. and

STATEMENT-2: The rms speed of molecules of a gas is equal to $\sqrt{\frac{3 R T}{M}}$ , where T and M are the temperature and molecular mass of the gas. R is the ideal gas constant.

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
Statement-1 is True, Statement-2 is False.
Statement-1 is False, Statement-2 is True.

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(4)

$V_{avg}, V_{rms}, V_{mp} will all exist at a particular temperature.$

Q 19 :

P - T curve for a cyclic process is as shown

P - V graph for this process will be:

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(4)

⇒ Slope of line joining origin to that point $\propto \frac{1}{V}$

As the slope of line OE is greater than the slope of line OC, SO, volume at 'E' is less than that at 'C'.

Therefore, answer is (4).

Q 20 :

A mixture of carbon dioxide and oxygen has volume 8310 ${cm}^{3}$ , temperature 300 K, pressure 100 kPa and mass 13.2 g. The number of moles of carbon dioxide and oxygen gases in the mixture respectively are ______.

(Assume both carbon dioxide and oxygen gases behave like ideal gases) [R = 8.31 J/mol.K] [2026]

0.15 and 0.18
0.25 and 0.08
0.21 and 0.12
0.13 and 0.20

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(3)

$Total number of moles in the mixture$

$(n_{1} + n_{2}) = \frac{P V}{R T} = \frac{10^{5} \times 8.31 \times 10^{- 3}}{8.31 \times 300} = \frac{1}{3} mole \approx 0.333 mole$

$Mole equation: n_{1} + n_{2} = \frac{1}{3} \approx 0.333 mole$ $. . . (i)$

$Mass equation: 44 n_{1} + 32 n_{2} = 13.2$ $. . . (i i)$

$({where 44 and 32 are the molar masses of CO}_{2} {and O}_{2} respectively)$

$On solving eq. (i) and eq. (ii)$

$44 n_{1} + 32 (0.333 - n_{1}) = 13.2$

$44 n_{1} + 10.667 - 32 n_{1} = 13.2$

$∵$ $12 n_{1} = 2.533$

$n_{1} \approx 0.211 mol$

$then, calculate n_{2}$

$n_{2} = 0.333 - 0.211$

$n_{2} = 0.122 mol$

Q 21 :

One gas of $n_{1}$ mole of molecules at temperature $T_{1}$ , volume $V_{1}$ , and pressure $P_{1}$ , and another gas of $n_{2}$ mole of molecules at temperature $T_{2}$ , volume $V_{2}$ , and pressure $P_{2}$ , are mixed resulting in pressure $P$ and volume $V$ of the mixture. The temperature of the mixture is ______. [2026]

$\frac{(T_{1} + T_{2})}{2}$
$\frac{T_{1} T_{2} P V}{(T_{2} P_{1} V_{1} + T_{1} P_{2} V_{2})}$
$(T_{2} P_{1} V_{1} + T_{1} P_{2} V_{2}) (T_{1} T_{2} P V)$
$\frac{| T_{1} - T_{2} |}{2}$

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(2)

$n_{total} = n_{1} + n_{2}$

$P V = n R T \Rightarrow n = \frac{P V}{R T}$

$\frac{P V}{T_{final}} = \frac{P_{1} V_{1}}{T_{1}} + \frac{P_{2} V_{2}}{T_{2}}$

$T_{final} = \frac{T_{1} T_{2} P V}{P_{1} V_{1} T_{2} + P_{2} V_{2} T_{1}}$

Q 22 :

An ideal gas undergoes a process maintaining relation between pressure (P) and volume (V) as $P = P_{0} (1 + {{(\frac{V_{0}}{V})}^{2})}^{- 1},$ where $P_{0}$ and $V_{0}$ are constants.

If two samples A and B (two moles each) with initial volume $V_{0}$ and $3 V_{0}$ respectively undergo above mentioned process and attain same pressure, then the difference at the temperatures of these samples, $T_{B} - T_{A}$ is _______. (R = gas constant) [2026]

$\frac{9 P_{0} V_{0}}{8 R}$
$\frac{11 P_{0} V_{0}}{10 R}$
$\frac{7 P_{0} V_{0}}{6 R}$
$\frac{13 P_{0} V_{0}}{11 R}$

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(2)

$P V = n R T \Rightarrow T = \frac{P V}{n R}$

$T = \frac{P_{0}}{n R} {[1 + {(\frac{V_{0}}{V})}^{2}]}^{- 1} V =$ $\frac{P_{0} V}{n R (1 + {(\frac{V_{0}}{V})}^{2})}$

$For sample A: T_{A} = \frac{P_{0} V_{0}}{2 R \cdot 2} = \frac{P_{0} V_{0}}{4 R}$

$For sample B: T_{B} = \frac{P_{0} 3 V_{0}}{2 R [1 + \frac{1}{9}]} = \frac{27 P_{0} V_{0}}{20 R}$

$T_{B} - T_{A} = \frac{P_{0} V_{0}}{R} [\frac{27}{20} - \frac{1}{4}] = \frac{11 P_{0} V_{0}}{10 R}$

Q 23 :

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: If the average kinetic energy of $H_{2}$ and $O_{2}$ molecules, kept in two different sized containers are same, then their temperatures will be same.

Reason R: The r.m.s. speed of $H_{2}$ and $O_{2}$ molecules are same at same temperature.

Choose the correct answer from the options given below: [2026]

Both A and R are true and R is the correct explanation of A
Both A and R are true but R is NOT the correct explanation of A
A is true but R is false
A is false but R is true

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(3)

$Avg. kinetic energy of molecule will be \frac{f}{2} K T$

$But v_{rms} = \sqrt{\frac{3 R T}{M}}$

$Since the molar masses are different, the v_{rms} values are different.$

Q 24 :

Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure 90 kPa and temperature 400 K. Keeping the temperature of one vessel constant at 400 K, the second vessel temperature is raised to 500 K. The final pressure in the vessels is ______ kPa. [2026]

100
120
90
105

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(1)

$Using mole conservation: n_{total} = n_{1} + n_{2}$

$\frac{P_{f} V}{T_{f}} + \frac{P_{f} V}{T_{f}} = \frac{P_{i} V}{T_{i}} + \frac{P_{i} V}{T_{i}}$

$P_{f} V (\frac{1}{400} + \frac{1}{500}) = \frac{2 P_{i} V}{T_{i}}$

$P_{f} \times V \times \frac{900}{400 \times 500} = \frac{2 \times 90 \times 10^{3} \times V}{400}$

$P_{f} = \frac{180 \times 10^{3} \times 5}{9} = 180 \times 10^{3} Pa = 100 kPa$

Q 25 :

If 2 mole of an ideal monoatomic gas at temperature T, is mixed with 6 mole of another ideal monoatomic gas at temperature 2T then the temperature of mixture is [2026]

$\frac{5}{2} T$
$\frac{5}{4} T$
$\frac{7}{2} T$
$\frac{7}{4} T$

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(4)

$T_{mix} = \frac{n_{1} C_{1} T_{1} + n_{2} C_{2} T_{2}}{n_{1} C_{1} + n_{2} C_{2}}$

$= \frac{(2 \times \frac{3}{2} R \times T) + (6 \times \frac{3}{2} R \times 2 T)}{(2 \times \frac{3}{2} R) + (6 \times \frac{3}{2} R)}$

$T_{mix} = \frac{2 T + 12 T}{8} = \frac{7}{4} T$

Topic Question Set

Q 11 :

A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature 50 °C. The gas is now heated to double its temperature. The modified pressure is ____ Pa. [2026]

Q 12 :

The mean free path of a molecule of diameter $5 \times 10^{- 10} m$ at the temperature $41 ° C$ and pressure $1.38 \times 10^{5} Pa$ is given as ______ m.

(Given $k_{B} = 1.38 \times 10^{- 23} J/K$ ) [2026]

Q 14 :

One mole of an ideal gas passes through a process where pressure and volume obey the pressure $P = P_{0} [1 - \frac{1}{2} {(\frac{V_{0}}{V})}^{2}]$ . Here $P_{0}$ and $V_{0}$ are constants. Calculate the change in the temperature of the gas, if its volume changes from $V_{0}$ to $2 V_{0}$ .

Q 15 :

The number density of molecules of a gas depends on their distance $' r'$ from the origin as, $n (r) = n_{0} e^{- α r^{4}}$ . Then the total number of molecules is proportional to:

Q 16 :

Number of collisions per second of molecules of a gas on the wall of a container per $m^{2}$ will:

Q 18 :

STATEMENT-1: Each molecule of a gas moves with rms speed if the temperature of gas is constant. and

STATEMENT-2: The rms speed of molecules of a gas is equal to $\sqrt{\frac{3 R T}{M}}$ , where T and M are the temperature and molecular mass of the gas. R is the ideal gas constant.

Q 19 :

P - T curve for a cyclic process is as shown

P - V graph for this process will be:

Q 25 :

If 2 mole of an ideal monoatomic gas at temperature T, is mixed with 6 mole of another ideal monoatomic gas at temperature 2T then the temperature of mixture is [2026]

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Topic Question Set

Q 11 : A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature 50 °C. The gas is now heated to double its temperature. The modified pressure is ____ Pa. [2026]

Q 12 : The mean free path of a molecule of diameter 5×10-10 m at the temperature 41°C and pressure 1.38×105 Pa is given as ______ m. (Given kB=1.38×10-23 J/K) [2026]

Q 14 : One mole of an ideal gas passes through a process where pressure and volume obey the pressure P=P0[1-12(V0V)2]. Here P0 and V0 are constants. Calculate the change in the temperature of the gas, if its volume changes from V0 to 2V0.

Q 15 : The number density of molecules of a gas depends on their distance 'r' from the origin as, n(r)=n0e-αr4. Then the total number of molecules is proportional to:

Q 16 : Number of collisions per second of molecules of a gas on the wall of a container per m2 will:

Q 18 : STATEMENT-1: Each molecule of a gas moves with rms speed if the temperature of gas is constant. and STATEMENT-2: The rms speed of molecules of a gas is equal to 3RTM, where T and M are the temperature and molecular mass of the gas. R is the ideal gas constant.

Q 19 : P - T curve for a cyclic process is as shown P - V graph for this process will be:

Q 21 : One gas of n1 mole of molecules at temperature T1, volume V1, and pressure P1, and another gas of n2 mole of molecules at temperature T2, volume V2, and pressure P2, are mixed resulting in pressure P and volume V of the mixture. The temperature of the mixture is ______. [2026]

Q 25 : If 2 mole of an ideal monoatomic gas at temperature T, is mixed with 6 mole of another ideal monoatomic gas at temperature 2T then the temperature of mixture is [2026]

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Q 11 :

A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature 50 °C. The gas is now heated to double its temperature. The modified pressure is ____ Pa. [2026]

Q 12 :

The mean free path of a molecule of diameter $5 \times 10^{- 10} m$ at the temperature $41 ° C$ and pressure $1.38 \times 10^{5} Pa$ is given as ______ m.

(Given $k_{B} = 1.38 \times 10^{- 23} J/K$ ) [2026]

Q 14 :

One mole of an ideal gas passes through a process where pressure and volume obey the pressure $P = P_{0} [1 - \frac{1}{2} {(\frac{V_{0}}{V})}^{2}]$ . Here $P_{0}$ and $V_{0}$ are constants. Calculate the change in the temperature of the gas, if its volume changes from $V_{0}$ to $2 V_{0}$ .

Q 15 :

The number density of molecules of a gas depends on their distance $' r'$ from the origin as, $n (r) = n_{0} e^{- α r^{4}}$ . Then the total number of molecules is proportional to:

Q 16 :

Number of collisions per second of molecules of a gas on the wall of a container per $m^{2}$ will:

Q 18 :

STATEMENT-1: Each molecule of a gas moves with rms speed if the temperature of gas is constant. and

STATEMENT-2: The rms speed of molecules of a gas is equal to $\sqrt{\frac{3 R T}{M}}$ , where T and M are the temperature and molecular mass of the gas. R is the ideal gas constant.

Q 19 :

P - T curve for a cyclic process is as shown

P - V graph for this process will be:

Q 25 :

If 2 mole of an ideal monoatomic gas at temperature T, is mixed with 6 mole of another ideal monoatomic gas at temperature 2T then the temperature of mixture is [2026]