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Assertion: Between two thermodynamic sta...

Assertion: Between two thermodynamic states, the value of (Q-W) is constant for any process.
Reason: Q and W are path functions.

A

(a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.

B

(b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

C

(c) If Assertion is true, but the Reason is false.

D

(d) If Assertion is false but the Reason is true.

Text Solution

AI Generated Solution

The correct Answer is:
To analyze the given assertion and reason, let's break it down step by step: ### Step 1: Understand the Assertion The assertion states that "Between two thermodynamic states, the value of (Q - W) is constant for any process." ### Step 2: Apply the First Law of Thermodynamics According to the first law of thermodynamics, we have: \[ Q = \Delta U + W \] Where: - \( Q \) is the heat added to the system, - \( W \) is the work done by the system, - \( \Delta U \) is the change in internal energy. From this equation, we can rearrange it to express \( Q - W \): \[ Q - W = \Delta U \] ### Step 3: Analyze the Change in Internal Energy The change in internal energy \( \Delta U \) depends only on the initial and final states of the system, not on the path taken to get from one state to another. Therefore, for any process between two thermodynamic states, \( \Delta U \) remains constant. ### Step 4: Conclusion on the Assertion Since \( Q - W = \Delta U \) and \( \Delta U \) is constant between two states, we conclude that the assertion is true. ### Step 5: Understand the Reason The reason states that "Q and W are path functions." This means that the values of \( Q \) and \( W \) depend on the specific path taken during the process, rather than just the initial and final states. ### Step 6: Analyze the Reason While it is true that \( Q \) and \( W \) are path functions, this does not contradict the assertion. The assertion is concerned with the difference \( Q - W \), which relates to the state function \( \Delta U \). ### Step 7: Conclusion on the Reason Both the assertion and the reason are true, but the reason does not correctly explain the assertion. The assertion is based on the constancy of \( \Delta U \), while the reason discusses the nature of \( Q \) and \( W \). ### Final Conclusion - Assertion: True - Reason: True, but not the correct explanation for the assertion. Thus, the correct answer is that both the assertion and reason are true, but the reason is not the correct explanation of the assertion.
To analyze the given assertion and reason, let's break it down step by step: ### Step 1: Understand the Assertion The assertion states that "Between two thermodynamic states, the value of (Q - W) is constant for any process." ### Step 2: Apply the First Law of Thermodynamics According to the first law of thermodynamics, we have: \[ Q = \Delta U + W \] ...
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