Oxygen is filled in a closed metal jar of volume 1 . 0 × 10 − 3 m 3 at a pressure of 1 . 5 × 10 5 Pa and temperature 400 K . The jar has a small leak in it. The atmospheric pressure is 1 . 0 × 10 5 Pa , and the atmospheric temperature is 300 K . Find the mass of the gas that leaks out by the time the pressure and the temperature inside the jar equalize with the surrounding.

Given that, inside the jar: Volume V 1 = 10 - 3 m 3 . Pressure P 1 = 1 . 5 × 10 5 Pa . Temperature T 1 = 400 K . Outside the jar: Atmospheric pressure P 2 = 1 × 10 5 Pa . Atmospheric temperature T 2 = 300 K . As we know, the molar mass M of oxygen is, = 32 gm = 32 × 10 - 3 kg Using the ideal gas equation, the number of moles in the jar, initially, n 1 = P 1 V 1 R T 1 Where P 1 = P 2 . To calculate the volume of gas, P 1 V 1 T 1 = P 2 V 2 T 2 V 2 = P 1 V 1 T 2 P 2 T 1 = 1 . 5 × 10 5 × 10 - 3 × 300 1 × 10 5 × 400 = 1 . 125 × 10 - 3 m 3 Hence, the net volume of the leaked gas, V = V 2 - V 1 = 1 . 125 × 10 - 3 - 1 × 10 - 3 = 1 . 25 × 10 - 4 m 3 Let n 2 be the number of moles of the leaked gas, ⇒ n 2 = P 2 V R T 2 = 1 × 10 5 × 1 . 25 × 10 - 4 8 . 3 × 300 = 0 . 005 Mass of the leaked gas=Number of moles×Molar mass ⇒ n 2 M = 0 . 005 × 32 = 0 . 16 g

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What is Avogadro's law?

Important Questions on Kinetic Theory of Gases

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Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory and Gas Laws

What is the average kinetic energy of molecules of an ideal gas leaking freely through an orifice of a container which has

N

molecules at pressure

P

in volume

V

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory and Gas Laws

Number of molecules in a volume of

4 {cm}^{3}

of a perfect monoatomic gas at some temperature

T

and at a pressure of

2 cm

of mercury is close to? (Given, mean kinetic energy of a molecule (at T) is

4 \times 10^{- 14} erg, g = 980 cm s^{- 2}

density of mercury

= 13.6 g {cm}^{- 3}

)

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory and Gas Laws

Two vessels separately contain two ideal gases

A

and

B

at the same temperature, the pressure of

A

being twice that of

B

. Under such conditions, the density of

A

is found to be

1.5

times the density of

B

. The ratio of molecular weights of

A

and

B

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory and Gas Laws

Oxygen is filled in a closed metal jar of volume

1.0 \times 10^{- 3} m^{3}

at a pressure of

1.5 \times 10^{5} Pa

and temperature

400 K

. The jar has a small leak in it. The atmospheric pressure is

1.0 \times 10^{5} Pa

, and the atmospheric temperature is

300 K

. Find the mass of the gas that leaks out by the time the pressure and the temperature inside the jar equalize with the surrounding.

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory and Gas Laws

An electric bulb of volume

250 cc

was sealed during manufacturing at a pressure of

10^{- 3} mm

of mercury at

27 ° C

. Compute the number of air molecules contained in the bulb. Avogadro's constant is

6 \times 10^{23} {mol}^{- 1}

, the density of mercury is

13600 kg m^{- 3}

and

g = 10 m s^{- 2}

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory and Gas Laws

Volume-temperature graph at atmospheric pressure for a monoatomic gas ( $V i n m^{3}, T i n ℃)$ is

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory and Gas Laws

Area of piston is $1 m^{2}$ . When heat is supplied to the gas it expands and displaces piston by $\frac{L}{2}$ , where $L = 1 m$ . Natural length of springs is $L = 1 m$ . Spring constant $K = 100 N m^{- 1}$ . The pressure of gas in final situation is – (considering equilibrium)

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EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory and Gas Laws

The temperature and pressure at Shimla are

15.0 ° C

and

72.0 cm

of mercury, and at Kalka, these are

35.0 ° C

and

76.0 cm

of mercury. Find the ratio of air density at Kalka to the air density at Simla.

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory and Gas Laws

A blend of nitrogen and water vapour is admitted to a flask at $760 torr$ , which contains a sufficient solid drying agent. After a long time, the pressure reached a steady value of $722 torr .$ If the experiment is done at $27 ° C$ and drying agent in weight increases by $0.9 g$ , determine the volume of the flask. Also, neglect any possible vapour pressure of drying agent and volume occupied by the drying agent.

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory and Gas Laws

An ideal gas undergoes an expansion from a state with temperature $T_{1}$ and volume $V_{1}$ through three different polytropic processes $A, B$ and $C$ as shown in the $P - V$ diagram. If $|Δ E_{A}|, |Δ E_{B}|$ and $|Δ E_{C}|$ be the magnitude of change in internal energy along the three paths respectively, then
Question Image

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory and Gas Laws

A partition divides a container having insulated walls into two compartments

I

and

II

. The same gas fills the two compartments whose initial parameters are given. The partition is a conducting wall which can move freely without friction. Which of the following statements is/are correct, with reference to the final equilibrium position?
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EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory and Gas Laws

Calculate the volume of

1 mole

of an ideal gas at STP.

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory and Gas Laws

The temperature of a gas contained in a closed vessel of constant volume increases by $1 ° C$ when the pressure of the gas is increased by $1 %$ . The initial temperature of the gas is

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory and Gas Laws

Find the number of molecules in

1 {cm}^{3}

of an ideal gas at

0 ° C

, at a pressure of

10^{- 5} mm

of mercury.

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory and Gas Laws

Two containers of the equal volume contain the same gas at pressure

P_{1}

and

P_{2}

and absolute temperatures

T_{1}

and

T_{2}

, respectively. On joining the vessels, the gas reaches a common pressure

P

and common temperature

T

. The ratio

\frac{P}{T}

is equal to

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory and Gas Laws

V

versus

T

curves at constant pressure

P_{1}

and

P_{2}

for an ideal gas are shown in figure. Here,

Question Image

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory and Gas Laws

Two identical glass bulbs are interconnected by a thin glass tube at $0 °C$ . A gas is filled in these bulbs. If one bulb is placed in ice and another bulb is placed in hot bath, the pressure of the gas become $1.5$ times. The temperature of hot bath will be.

Question Image

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory and Gas Laws

A ring-shaped tube contains two ideal gases with equal masses and molar masses M₁ = 32 and M₂ = 28. The gases are separated by one fixed partition and another movable stopper S which can move freely without friction inside the ring. The angle $α$ is

Question Image

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory and Gas Laws

A vessel has

6 g

of oxygen at pressure

P

and temperature

400 K .

A small hole is made in it, so that oxygen leaks out. How much oxygen leaks out if the final pressure is

\frac{P}{2}

and temperature is

300 K

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Kinetic Theory and Gas Laws

A flask is filled with

13 g

of an ideal gas at

27 ° C

and its temperature is raised to

52 ° C

. The mass of the gas that has to be released to maintain the temperature of the gas in the flask at

52 ° C

, the pressure remaining the same is

What is Avogadro's law?

Important Questions on Kinetic Theory of Gases

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