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A thermally isolated cylinder is divided into 2 compartments by a thermally conductive piston. Initially, piston divides the cylinder into two compartments, A and B, of equal volume V /2 and temperature T0 = 200 K. One mole of monatomic gas is in each compartment. An external agent slowly moves the piston to the side until the volumes are V /3 and 2V /3. Throughout this process, the temperature remains uniform. The final temperature = X 3rise to (2/3)Kelwin . Calculate X.?
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A thermally isolated cylinder is divided into 2 compartments by a ther...
Introduction
In this problem, we are given a thermally isolated cylinder divided into two compartments, A and B, by a thermally conductive piston. Initially, the compartments have equal volume and temperature, and each compartment contains one mole of monatomic gas. We are asked to determine the final temperature of the system after the piston is moved to change the volumes of the compartments.

Given Information
- Initial temperature (T0) = 200 K
- Initial volume of each compartment (V / 2)
- Final volume of compartment A (V / 3)
- Final volume of compartment B (2V / 3)

Approach
To solve this problem, we can use the First Law of Thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. Since the process is adiabatic (no heat exchange with the surroundings), the change in internal energy is equal to the work done by the system.

We can calculate the work done by the system as the area under the pressure-volume (P-V) curve. The pressure in each compartment is given by the ideal gas law: P = nRT / V, where n is the number of moles, R is the gas constant, and T is the temperature. By substituting the given values, we can find the initial and final pressures in each compartment.

Since the temperature remains constant throughout the process, the final temperature (X) can be calculated using the ideal gas law: P_final = nRT_final / V_final, where P_final is the final pressure in each compartment.

Calculation
1. Initial pressure in each compartment:
- P_initial_A = nRT0 / (V / 2)
- P_initial_B = nRT0 / (V / 2)

2. Final pressure in each compartment:
- P_final_A = nRT_final / (V / 3)
- P_final_B = nRT_final / (2V / 3)

3. Work done by the system:
- W = P_final_A * (V / 3 - V / 2) + P_final_B * (2V / 3 - V / 2)

4. Equating the work done to the change in internal energy:
- W = ΔU = U_final - U_initial

5. Since the temperature remains constant, the change in internal energy is zero:
- U_final - U_initial = 0

6. Solving for the final temperature:
- X = T_final = U_final * (V / 2) / (nR)

Conclusion
The final temperature of the system is given by X = U_final * (V / 2) / (nR), where U_final is the change in internal energy of the system, V is the final volume of each compartment, n is the number of moles, and R is the gas constant. By calculating the initial and final pressures in each compartment and using the First Law of Thermodynamics, we can find the work done by the system and determine the final temperature.
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Paragraph for Questions 13 & 14In the figure a container is shown to have a movable (without friction) piston on top. The container andthe piston are all made of perfectly insulating material allowing no heat transfer between outside andinside the container. The container is divided into two compartments by a rigid partition made of athermally conducting material that allows slow transfer of heat. The lower compartment of the containeris filled with 2 moles of an ideal monatomic gas at 700 K and the upper compartment is filled with 2moles of an ideal diatomic gas at 400 K. The heat capacities per mole of an ideal monatomic gas areand those for an ideal diatomic gas are Q.Consider the partition to be rigidly fixed so that it does not move. When equilibrium is achieved, the finaltemperature of the gases will be

In the figure a container is shown to have a movable (without friction) piston on top. The container andthe piston are all made of perfectly insulating material allowing no heat transfer between outside andinside the container. The container is divided into two compartments by a rigid partition made of athermally conducting material that allows slow transfer of heat. The lower compartment of the container is filled with 2 moles of an ideal monatomic gas at 700 K and the upper compartment is filled with 2 moles of an ideal diatomic gas at 400 K. The heat capacities per mole of an ideal monatomic gas areand those for an ideal diatomic gas are Q.Now consider the partition to be free to move without friction so that the pressure of gases in bothcompartments is the same. Then total work done by the gases till the time they achieve equilibrium will be

In the figure, a container is shown to have a movable (without friction) piston on top. The container and the piston are all made of perfectly insulated material allowing no heat transfer between outside and inside the container. The container is divided into two compartments by a rigid partition made of a thermally conducting material that allows slow transfer of heat. The lower compartment of the container is filled with 2 moles of an ideal monatomic gas at 700 K and the upper compartment is filled with 2 moles of an ideal diatomic gas at 400 K. The heat capacities per mole of an ideal monatomic gas arethose for an ideal diatomic gas areQ.8.Now consider the partition to be free to move without friction so that the pressure of gases in both compartments is the same. The total work done by the gases till the time they achieve equilibrium will be

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A thermally isolated cylinder is divided into 2 compartments by a thermally conductive piston. Initially, piston divides the cylinder into two compartments, A and B, of equal volume V /2 and temperature T0 = 200 K. One mole of monatomic gas is in each compartment. An external agent slowly moves the piston to the side until the volumes are V /3 and 2V /3. Throughout this process, the temperature remains uniform. The final temperature = X 3rise to (2/3)Kelwin . Calculate X.?
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A thermally isolated cylinder is divided into 2 compartments by a thermally conductive piston. Initially, piston divides the cylinder into two compartments, A and B, of equal volume V /2 and temperature T0 = 200 K. One mole of monatomic gas is in each compartment. An external agent slowly moves the piston to the side until the volumes are V /3 and 2V /3. Throughout this process, the temperature remains uniform. The final temperature = X 3rise to (2/3)Kelwin . Calculate X.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A thermally isolated cylinder is divided into 2 compartments by a thermally conductive piston. Initially, piston divides the cylinder into two compartments, A and B, of equal volume V /2 and temperature T0 = 200 K. One mole of monatomic gas is in each compartment. An external agent slowly moves the piston to the side until the volumes are V /3 and 2V /3. Throughout this process, the temperature remains uniform. The final temperature = X 3rise to (2/3)Kelwin . Calculate X.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thermally isolated cylinder is divided into 2 compartments by a thermally conductive piston. Initially, piston divides the cylinder into two compartments, A and B, of equal volume V /2 and temperature T0 = 200 K. One mole of monatomic gas is in each compartment. An external agent slowly moves the piston to the side until the volumes are V /3 and 2V /3. Throughout this process, the temperature remains uniform. The final temperature = X 3rise to (2/3)Kelwin . Calculate X.?.
Solutions for A thermally isolated cylinder is divided into 2 compartments by a thermally conductive piston. Initially, piston divides the cylinder into two compartments, A and B, of equal volume V /2 and temperature T0 = 200 K. One mole of monatomic gas is in each compartment. An external agent slowly moves the piston to the side until the volumes are V /3 and 2V /3. Throughout this process, the temperature remains uniform. The final temperature = X 3rise to (2/3)Kelwin . Calculate X.? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
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