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  4. In a cylindrical container of sufficiently large height, two easily moving pistons enclose certain amount of same ideal gas in two chambers as shown in the figure-2.43. <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/b00eb554dfb6a2d04c8585e9a3bd107a-.png /> The upper piston is at a height 20 cm from the bottom and lower piston is at a height 8 cm from the bottom. The mass of each piston is m kg and cross sectional area of each piston is A m2 where (m g/A)=P0 and P0 is the atmospheric pressure =1 × 105 N / m 2. The cylindrical container and pistons are made of conducting material. Initially the temperature of gas is 27° C and whole system is in equilibrium. Now if the upper piston is slowly lifted by 16 cm and held in that position with the help of some external force. As a result, the lower piston rises slowly by l cm. In a cylindrical container of sufficiently large height, two easily moving pistons enclose certain amount of same ideal gas in two chambers as shown in the figure-2.43. <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/b00eb554dfb6a2d04c8585e9a3bd107a-.png /> The upper piston is at a height 20 cm from the bottom and lower piston is at a height 8 cm from the bottom. The mass of each piston is m kg and cross sectional area of each piston is A m2 where (m g/A)=P0 and P0 is the atmospheric pressure =1 × 105 N / m 2. The cylindrical container and pistons are made of conducting material. Initially the temperature of gas is 27° C and whole system is in equilibrium. Now if the upper piston is slowly lifted by 16 cm and held in that position with the help of some external force. As a result, the lower piston rises slowly by l cm. The value of l is :

Q. In a cylindrical container of sufficiently large height, two easily moving pistons enclose certain amount of same ideal gas in two chambers as shown in the figure-2.43.

The upper piston is at a height from the bottom and lower piston is at a height from the bottom. The mass of each piston is m kg and cross sectional area of each piston is where and is the atmospheric pressure .
The cylindrical container and pistons are made of conducting material. Initially the temperature of gas is and whole system is in equilibrium. Now if the upper piston is slowly lifted by and held in that position with the help of some external force. As a result, the lower piston rises slowly by . In a cylindrical container of sufficiently large height, two easily moving pistons enclose certain amount of same ideal gas in two chambers as shown in the figure-2.43.

The upper piston is at a height from the bottom and lower piston is at a height from the bottom. The mass of each piston is m kg and cross sectional area of each piston is where and is the atmospheric pressure .
The cylindrical container and pistons are made of conducting material. Initially the temperature of gas is and whole system is in equilibrium. Now if the upper piston is slowly lifted by and held in that position with the help of some external force. As a result, the lower piston rises slowly by .
The value of is :

Kinetic Theory Report Error

Solution:

Let and be the initial pressure in lower chamber of gas and upper chamber of gas.

If and are final pressure and volume in upper chamber



Now consider lower chamber

and

and



Solving we get


Questions from Kinetic Theory

1. Which one of the following is not an assumption in the kinetic theory of gases?

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2. A gas at one atmosphere and 100 mL is mixed with another gas of equal moles at 0.5 atm and having volume 50 mL in flask of 1 L. What is their final pressure?

3. Two moles of monoatomic gas is mixed with three moles of a diatomic gas. The molar specific heat of the mixture at constant volume is

4. At what temperature is the root mean square speed of an atom in an argon gas cylinder equal to the rms speed of a helium gas atom at - ? (Atomic mass of and )

5. In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation , where is a constant. In this process the temperature of the gas is incresed by . The amount of heat absorbed by gas is (R is gas constant) :

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