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A rigid and thermally isolated tank is divided into two compartments of equal volume V, separated by a thin membrane. One compartment contains one mole of an ideal gas A and the other compartment contains one mole of a different ideal gas B. The two gases are in thermal equilibrium at a temperature T. If the membrane ruptures, the two gases mix. Assume that the gases are chemically inert. The change in the total entropy of the gases on mixing is
- a)0
- b)R ln 2
- c)3/2R ln 2
- d)2R ln 2
Correct answer is option 'D'. Can you explain this answer?
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A rigid and thermally isolated tank is divided into two compartments o...
Introduction:
In this scenario, we have a rigid and thermally isolated tank divided into two compartments, each containing one mole of different ideal gases A and B. The gases are in thermal equilibrium at a temperature T. When the membrane separating the compartments ruptures, the gases mix. We need to find the change in the total entropy of the gases upon mixing.
Explanation:
First Law of Thermodynamics:
The first law of thermodynamics 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. Mathematically, it can be written as:
ΔU = Q - W
Entropy:
Entropy is a measure of the disorder or randomness in a system. It is given by the equation:
ΔS = Q/T
Change in Internal Energy:
Since the gases are in thermal equilibrium, their temperatures are the same. Therefore, there is no change in internal energy (ΔU = 0) upon mixing.
Change in Entropy:
The change in entropy can be calculated using the equation:
ΔS = Q/T
Heat Transfer:
When the gases mix, heat is transferred between them until they reach a new equilibrium temperature. Since the gases are ideal and chemically inert, no heat is generated or absorbed during the mixing process. Therefore, the heat transferred (Q) is zero.
Change in Entropy Equation:
Using the equation ΔS = Q/T and substituting Q = 0, we get:
ΔS = 0/T
ΔS = 0
Total Entropy Change:
The change in total entropy (ΔStotal) is given by the sum of the individual entropy changes of the gases. Since both gases are in thermal equilibrium at the same temperature T, their individual entropy changes are also zero. Therefore, the change in total entropy is zero.
Final Answer:
The correct answer is option 'a) 0'. The change in the total entropy of the gases upon mixing is zero.
In this scenario, we have a rigid and thermally isolated tank divided into two compartments, each containing one mole of different ideal gases A and B. The gases are in thermal equilibrium at a temperature T. When the membrane separating the compartments ruptures, the gases mix. We need to find the change in the total entropy of the gases upon mixing.
Explanation:
First Law of Thermodynamics:
The first law of thermodynamics 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. Mathematically, it can be written as:
ΔU = Q - W
Entropy:
Entropy is a measure of the disorder or randomness in a system. It is given by the equation:
ΔS = Q/T
Change in Internal Energy:
Since the gases are in thermal equilibrium, their temperatures are the same. Therefore, there is no change in internal energy (ΔU = 0) upon mixing.
Change in Entropy:
The change in entropy can be calculated using the equation:
ΔS = Q/T
Heat Transfer:
When the gases mix, heat is transferred between them until they reach a new equilibrium temperature. Since the gases are ideal and chemically inert, no heat is generated or absorbed during the mixing process. Therefore, the heat transferred (Q) is zero.
Change in Entropy Equation:
Using the equation ΔS = Q/T and substituting Q = 0, we get:
ΔS = 0/T
ΔS = 0
Total Entropy Change:
The change in total entropy (ΔStotal) is given by the sum of the individual entropy changes of the gases. Since both gases are in thermal equilibrium at the same temperature T, their individual entropy changes are also zero. Therefore, the change in total entropy is zero.
Final Answer:
The correct answer is option 'a) 0'. The change in the total entropy of the gases upon mixing is zero.
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A rigid and thermally isolated tank is divided into two compartments o...
∆smix=nRlnV2/V1 as n =2;V2=2V1 then ∆smix=2Rln2
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A rigid and thermally isolated tank is divided into two compartments of equal volume V, separated by a thin membrane. One compartment contains one mole of an ideal gas A and the other compartment contains one mole of a different ideal gas B. The two gases are in thermal equilibrium at a temperature T. If the membrane ruptures, the two gases mix. Assume that the gases are chemically inert. The change in the total entropy of the gases on mixing isa)0b)R ln 2c)3/2R ln 2d)2R ln 2Correct answer is option 'D'. Can you explain this answer?
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A rigid and thermally isolated tank is divided into two compartments of equal volume V, separated by a thin membrane. One compartment contains one mole of an ideal gas A and the other compartment contains one mole of a different ideal gas B. The two gases are in thermal equilibrium at a temperature T. If the membrane ruptures, the two gases mix. Assume that the gases are chemically inert. The change in the total entropy of the gases on mixing isa)0b)R ln 2c)3/2R ln 2d)2R ln 2Correct answer is option 'D'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A rigid and thermally isolated tank is divided into two compartments of equal volume V, separated by a thin membrane. One compartment contains one mole of an ideal gas A and the other compartment contains one mole of a different ideal gas B. The two gases are in thermal equilibrium at a temperature T. If the membrane ruptures, the two gases mix. Assume that the gases are chemically inert. The change in the total entropy of the gases on mixing isa)0b)R ln 2c)3/2R ln 2d)2R ln 2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rigid and thermally isolated tank is divided into two compartments of equal volume V, separated by a thin membrane. One compartment contains one mole of an ideal gas A and the other compartment contains one mole of a different ideal gas B. The two gases are in thermal equilibrium at a temperature T. If the membrane ruptures, the two gases mix. Assume that the gases are chemically inert. The change in the total entropy of the gases on mixing isa)0b)R ln 2c)3/2R ln 2d)2R ln 2Correct answer is option 'D'. Can you explain this answer?.
A rigid and thermally isolated tank is divided into two compartments of equal volume V, separated by a thin membrane. One compartment contains one mole of an ideal gas A and the other compartment contains one mole of a different ideal gas B. The two gases are in thermal equilibrium at a temperature T. If the membrane ruptures, the two gases mix. Assume that the gases are chemically inert. The change in the total entropy of the gases on mixing isa)0b)R ln 2c)3/2R ln 2d)2R ln 2Correct answer is option 'D'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A rigid and thermally isolated tank is divided into two compartments of equal volume V, separated by a thin membrane. One compartment contains one mole of an ideal gas A and the other compartment contains one mole of a different ideal gas B. The two gases are in thermal equilibrium at a temperature T. If the membrane ruptures, the two gases mix. Assume that the gases are chemically inert. The change in the total entropy of the gases on mixing isa)0b)R ln 2c)3/2R ln 2d)2R ln 2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rigid and thermally isolated tank is divided into two compartments of equal volume V, separated by a thin membrane. One compartment contains one mole of an ideal gas A and the other compartment contains one mole of a different ideal gas B. The two gases are in thermal equilibrium at a temperature T. If the membrane ruptures, the two gases mix. Assume that the gases are chemically inert. The change in the total entropy of the gases on mixing isa)0b)R ln 2c)3/2R ln 2d)2R ln 2Correct answer is option 'D'. Can you explain this answer?.
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