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The P-V diagram below shows three possible paths for an ideal gas to reach the final state from an initial state i. Which among the following statements (3) is (are) correct?
(a) The work done by the gas is maximum along path-3.
(b) Minimum change in the internal energy occurs along path-2.
(c) Maximum heat transfer is for path - 1
(d) Heat transfer is path independent?
(a) The work done by the gas is maximum along path-3.
(b) Minimum change in the internal energy occurs along path-2.
(c) Maximum heat transfer is for path - 1
(d) Heat transfer is path independent?
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The P-V diagram below shows three possible paths for an ideal gas to r...
Analysis of the P-V Diagram Paths
To evaluate the statements regarding the work done, internal energy change, and heat transfer for an ideal gas transitioning between states in a P-V diagram, we need to consider the thermodynamic principles involved.
Work Done by the Gas
- The work done by an ideal gas during a process can be represented by the area under the curve on the P-V diagram.
- Path-3 likely represents the maximum area under the curve, indicating that the work done by the gas is maximum along this path. Thus, Statement (a) is correct.
Change in Internal Energy
- The change in internal energy (ΔU) for an ideal gas depends only on the initial and final states, not the path taken.
- Path-2 may suggest a smaller area under the curve, but since ΔU is state-dependent, the change remains the same regardless of the path. Therefore, the statement regarding minimum change in internal energy is misleading. Statement (b) is incorrect.
Heat Transfer
- Heat transfer (Q) varies with the process path. The maximum heat transfer generally occurs in paths where the temperature change is substantial and work done is less.
- Path-1 may involve more heat transfer if it maintains higher temperatures. However, without specific information about temperatures and pressures, this statement cannot be confirmed universally. Thus, Statement (c) may not be correct.
Path Independence of Heat Transfer
- According to the first law of thermodynamics, heat transfer is not path-independent. It depends on the process taken. Hence, Statement (d) is incorrect.
Conclusion
- Correct statements: (a) only.
- Statements (b), (c), and (d) are incorrect based on thermodynamic principles.
To evaluate the statements regarding the work done, internal energy change, and heat transfer for an ideal gas transitioning between states in a P-V diagram, we need to consider the thermodynamic principles involved.
Work Done by the Gas
- The work done by an ideal gas during a process can be represented by the area under the curve on the P-V diagram.
- Path-3 likely represents the maximum area under the curve, indicating that the work done by the gas is maximum along this path. Thus, Statement (a) is correct.
Change in Internal Energy
- The change in internal energy (ΔU) for an ideal gas depends only on the initial and final states, not the path taken.
- Path-2 may suggest a smaller area under the curve, but since ΔU is state-dependent, the change remains the same regardless of the path. Therefore, the statement regarding minimum change in internal energy is misleading. Statement (b) is incorrect.
Heat Transfer
- Heat transfer (Q) varies with the process path. The maximum heat transfer generally occurs in paths where the temperature change is substantial and work done is less.
- Path-1 may involve more heat transfer if it maintains higher temperatures. However, without specific information about temperatures and pressures, this statement cannot be confirmed universally. Thus, Statement (c) may not be correct.
Path Independence of Heat Transfer
- According to the first law of thermodynamics, heat transfer is not path-independent. It depends on the process taken. Hence, Statement (d) is incorrect.
Conclusion
- Correct statements: (a) only.
- Statements (b), (c), and (d) are incorrect based on thermodynamic principles.
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The P-V diagram below shows three possible paths for an ideal gas to reach the final state from an initial state i. Which among the following statements (3) is (are) correct?(a) The work done by the gas is maximum along path-3.(b) Minimum change in the internal energy occurs along path-2.(c) Maximum heat transfer is for path - 1(d) Heat transfer is path independent?
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The P-V diagram below shows three possible paths for an ideal gas to reach the final state from an initial state i. Which among the following statements (3) is (are) correct?(a) The work done by the gas is maximum along path-3.(b) Minimum change in the internal energy occurs along path-2.(c) Maximum heat transfer is for path - 1(d) Heat transfer is path independent? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The P-V diagram below shows three possible paths for an ideal gas to reach the final state from an initial state i. Which among the following statements (3) is (are) correct?(a) The work done by the gas is maximum along path-3.(b) Minimum change in the internal energy occurs along path-2.(c) Maximum heat transfer is for path - 1(d) Heat transfer is path independent? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The P-V diagram below shows three possible paths for an ideal gas to reach the final state from an initial state i. Which among the following statements (3) is (are) correct?(a) The work done by the gas is maximum along path-3.(b) Minimum change in the internal energy occurs along path-2.(c) Maximum heat transfer is for path - 1(d) Heat transfer is path independent?.
The P-V diagram below shows three possible paths for an ideal gas to reach the final state from an initial state i. Which among the following statements (3) is (are) correct?(a) The work done by the gas is maximum along path-3.(b) Minimum change in the internal energy occurs along path-2.(c) Maximum heat transfer is for path - 1(d) Heat transfer is path independent? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The P-V diagram below shows three possible paths for an ideal gas to reach the final state from an initial state i. Which among the following statements (3) is (are) correct?(a) The work done by the gas is maximum along path-3.(b) Minimum change in the internal energy occurs along path-2.(c) Maximum heat transfer is for path - 1(d) Heat transfer is path independent? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The P-V diagram below shows three possible paths for an ideal gas to reach the final state from an initial state i. Which among the following statements (3) is (are) correct?(a) The work done by the gas is maximum along path-3.(b) Minimum change in the internal energy occurs along path-2.(c) Maximum heat transfer is for path - 1(d) Heat transfer is path independent?.
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