GATE ME 2015 Set 1 — Question 64
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Thermodynamics → Laws & Properties → Ideal & Real Gas Behaviour
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Question
A well insulated rigid container of volume contains of an ideal gas [ and ] at a pressure of . A stirrer is rotated at constant rpm in the container for 1000 rotations and the applied torque is . The final temperature of the gas (in K) is ________.
Correct answer
1283.4 to 1287.4
Solution
The system is a rigid, insulated container. From the first law of thermodynamics for a closed system: . Since it is well insulated, . The work done by the stirrer on the gas is . This work is done on the system, so . Thus, . The gas constant . The initial temperature . Substituting the values: . Therefore, .
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