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Chapter 18: Problem 10

Which of the following statements is (are) true? a) When a system does work, its internal energy always decreases. b) Work done on a system always decreases its internal energy. c) When a system does work on its surroundings, the sign of the work is always positive. d) Positive work done on a system is always equal to the system's gain in internal energy. e) If you push on the piston of a gas-filled cylinder, the energy of the gas in the cylinder will increase.

Short Answer

Expert verified
Based on the analysis of the given statements, identify which statements are true and which are false regarding work and internal energy. a) False - When a system does work, its internal energy does not always decrease. b) False - Work done on a system does not always decrease its internal energy. c) True - When a system does work on its surroundings, the sign of the work is always positive. d) False - Positive work done on a system is not always equal to the system's gain in internal energy. e) True - If you push on the piston of a gas-filled cylinder, the energy of the gas in the cylinder will increase.

Step by step solution

01

Statement a)

This statement claims that when a system does work, its internal energy always decreases. According to the first law of thermodynamics, the change in internal energy (∆U) is equal to the heat added to the system (Q) minus the work done by the system (W): ∆U = Q - W. When a system does work (W > 0), it is possible for its internal energy to decrease if the heat added (Q) is less than the work done. However, it is not true in every case since the heat added can be greater than the work done, leading to an increase in internal energy. Therefore, statement a is false.
02

Statement b)

This statement claims that work done on a system always decreases its internal energy. According to the first law of thermodynamics, if work is done on a system, it means that an external force is doing work on the system to increase its internal energy. In this case, the work done (W) is negative. The equation ∆U = Q - W would become: ∆U = Q + |W|. Since both Q and |W| are positive, the internal energy should increase. Therefore, statement b is false.
03

Statement c)

This statement claims that when a system does work on its surroundings, the sign of the work is always positive. According to the sign convention, when a system does work on its surroundings (expands), the work done is considered positive (W > 0). When surroundings do work on the system (compresses), the work done is considered negative (W < 0). Therefore, statement c is true.
04

Statement d)

This statement claims that positive work done on a system is always equal to the system's gain in internal energy. Positive work done on a system means it's done by the surroundings leading to an increase in the system's internal energy. But the first law of thermodynamics (∆U = Q - W) tells us that the change in internal energy depends on both the heat added (Q) and the work done (W) on the system. If positive work is done on the system, it can contribute to an increase in internal energy but it is not always equal to the total gain in internal energy because the heat added (Q) will also affect the internal energy. Therefore, statement d is false.
05

Statement e)

This statement claims that if you push on the piston of a gas-filled cylinder, the energy of the gas in the cylinder will increase. When you push the piston of a gas-filled cylinder, you are performing work on the system which is the gas inside the cylinder. As a result of this work, the internal energy of the gas in the cylinder will increase (provided that there is no heat loss during this process). Therefore, statement e is true. In conclusion: a) False b) False c) True d) False e) True

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