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Some outside force does $450 \text{ J}$ of work compressing an ideal gas in a cylinder. During this compression, $120 \text{ J}$ of heat is transferred out of the gas in the surroundings by conduction. A student concludes that the internal energy of the gas increased by $330 \text{ J}$, but is not really sure why they can make this conclusion.

Which of the following statements identifies the correct conclusion with justification?

A

The student’s answer is correct, and justified by the first law of thermodynamics.

B

The student’s answer is correct, and justified by the second law of thermodynamics.

C

The student’s answer is incorrect. The internal energy of the gas actually decreases by $330 \text{ J}$.

D

The student’s answer is incorrect. The internal energy of the gas increases by $570 \text{ J}$.

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