GATE ME 2025 Set 1 — Question 18
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Thermodynamics → Laws & Properties → Carnot Cycle & Entropy
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Question
Air inside a rigid, thermally-insulated tank undergoes stirring as shown in the figure below. Which one of the following options is correct?
Correct answer
(C) Both the enthalpy and the entropy of the air increase
Solution
Let's analyze the process using the first and second laws of thermodynamics.First Law of Thermodynamics (Energy Conservation):
For a closed system, the first law is given by .
Given:
For a closed system, the change in entropy is given by , where is the entropy generation due to irreversibilities.Given:
For a closed system, the first law is given by .
Given:
- The tank is rigid, meaning its volume () is constant. Therefore, boundary work () is zero.
- The tank is thermally-insulated, meaning there is no heat transfer ().
- Stirring is performed, which is a form of work done on the system ( if work done by the system is positive, or if work done on the system is positive. Let's assume is work done by the system, so is negative, or we can write , where is work input).
For a closed system, the change in entropy is given by , where is the entropy generation due to irreversibilities.Given:
- (thermally-insulated).
- Stirring is an irreversible process. Therefore, entropy generation .
- Enthalpy of the air increases.
- Entropy of the air increases.
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