Question

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

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. Answer: c) and e) are true.

Step-by-step solution

Statement a: When a system does work, its internal energy always decreases.

To assess the validity of this statement, we consider the First Law of Thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W), or ΔU = Q - W. When a system does work, it is not necessarily true that its internal energy always decreases. If the heat added to the system is greater than the work done, the internal energy will increase (Q > W). On the other hand, if the heat added is less than the work done, the internal energy will decrease (Q < W). Therefore, statement a is false.

Statement b: Work done on a system always decreases its internal energy.

This statement is also related to the First Law of Thermodynamics, as mentioned before. When work is done on a system, the relation becomes ΔU = Q + W. If the work done on the system is positive and greater than the heat lost by the system (Q < 0), the internal energy of the system will decrease. However, if the work done is less than the heat gained (Q > 0), the internal energy will increase. Therefore, statement b is false.

Statement c: When a system does work on its surroundings, the sign of the work is always positive.

By convention, when a system does work on its surroundings, the work done (W) is considered positive. On the other hand, when work is done on the system, the work done is considered negative. Therefore, statement c is true.

Statement d: Positive work done on a system is always equal to the system's gain in internal energy.

This statement is not necessarily true. As mentioned before, the change in internal energy is given by ΔU = Q + W. Positive work done on a system may not always equal the system's gain in internal energy if some heat is lost or gained during the process. Therefore, statement d is false.

Statement e: If you push on the piston of a gas-filled cylinder, the energy of the gas in the cylinder will increase.

When you push on the piston of a gas-filled cylinder, you are doing work on the system (gas in the cylinder). According to the First Law of Thermodynamics, this work done on the system (W, which is negative because work is done on the system) can result in an increase in internal energy if it is greater than the heat loss (if any) during the process. While it is not always guaranteed that the energy of the gas will increase, in most practical cases it is reasonable to assume that applying work by pushing the piston results in an increase in energy. Therefore, statement e is true. In conclusion, statements c) and e) are true, while statements a), b), and d) are false.