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An ideal monatomic gas is confined in a cylinder by a spring-loaded piston of cross section $8.0 \times 10^{- 3} m^{2}$ . Initially the gas is at $300 K$ and occupies a volume of $2.4 \times 10^{- 3} m^{3}$ and the spring is in its relaxed state. The gas is heated by a small heater until the piston moves out slowly by $0.1 m$ . The final temperature of the gas is $N \times 100 K$ . Find the value of $N$ . The force constant of the spring is $8000 N m^{- 1}$ , and the atmospheric pressure is $1.0 \times 10^{5} N m^{- 2}$ . The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. Neglect any heat-loss through the lead wires of the heater. The heat capacity of the heater coil is negligible.

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Important Questions on Kinetic Theory of Gases

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IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 3 - Kinetic Theory of Gases>Exercises>Q 11

Consider a vertical tube open at both ends. The tube consists of two parts, each of different cross-sections and each part having a piston which can move smoothly in respective tubes. The two pistons are joined together by an inextensible wire. The combined mass of the two pistons is

5 kg

and area of cross-section of the upper piston is

10 {cm}^{2}

greater than that of the lower piston. Amount of gas enclosed by the pistons is one mole. When the gas is heated slowly, pistons move by

50 cm

. If the rise in the temperature of the gas is

\frac{15 x}{R}

, where

R

is universal gas constant. Find the value of

x

. Use

g = 10 m s^{- 2}

and outside pressure

= 10^{5} N m^{- 2}

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 3 - Kinetic Theory of Gases>Exercises>Q 12

$n$ moles of a gas in a cylinder under a piston are transferred to infinitely slowly from a state with a volume of $V_{0}$ and a pressure $3 P_{0}$ atoms to state with $3 V_{0}$ and a pressure $P_{0}$ as shown in figure. If the maximum temperature that the gas will reach in this process is $\frac{x P_{0} V_{0}}{n R}$ , what is the value of $x ?$

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Physics

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 3 - Kinetic Theory of Gases>Exercises>Q 13

Given figure shows a horizontal cylindrical container of length

30 c m

, which is partitioned by a tight-fitting separator. The separator is diathermic but conducts heat very slowly. Initially the separator is in the state shown in the figure. The temperature of left part of cylinder is

100 K

and that on right part is

400 K

. Initially the separator is in equilibrium. As heat is conducted from right to left part, separator displaces to the right. Find the displacement of separator (in

cm

) after a long time when gases on the two parts of cylinder are in thermal equilibrium.
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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 3 - Kinetic Theory of Gases>Exercises>Q 14

An ideal gas has a volume

0.3 m^{3}

150 kPa

. It is confined by a spring-loaded piston in a vertical cylinder. Initially, the spring is in relaxed state. If the gas is heated to a final state of

0.5 m^{3}

and pressure

600 kPa

, find the work done (in

kJ

) on the spring (atmospheric pressure,

P_{0} = 1 \times 10^{5} N m^{- 2}

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 3 - Kinetic Theory of Gases>Exercises>Q 15

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 (in

g

) of the gas that leaks out by the time the pressure and the temperature inside the jar equalise with the surrounding.

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 3 - Kinetic Theory of Gases>Exercises>Q 16

Figure shows a vertical cylindrical vessel separated in two parts by a frictionless piston free to move along the length of the vessel. The length of the cylinder is $1.0 m$ and the piston divides the cylinder in the ratio of $3 : 2$ . Each of the two parts of the vessel contains $0.2$ mole of an ideal gas. The temperature of the gas is $300 K$ in each part. Calculate the mass of the piston. (in $kg$ )

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PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 3 - Kinetic Theory of Gases>Archives>Q 1

One kilogram of a diatomic gas is at a pressure of

8 \times 10^{4} N m^{- 2}

. The density of the gas is

4 kg m^{- 3}

. What is the energy of the gas due to its thermal motion?

EASY

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 3 - Kinetic Theory of Gases>Archives>Q 2

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

Important Questions on Kinetic Theory of Gases

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