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Chapter 5: Problem 7

You may have noticed that when you compress the air in a bicycle pump, the body of the pump gets warmer. (a) Assuming the pump and the air in it comprise the system, what is the sign of \(w\) when you compress the air? (b) What is the sign of \(q\) for this process? (c) Based on your answers to parts (a) and (b), can you determine the sign of \(\Delta E\) for compressing the air in the pump? If not, what would you expect for the sign of \(\Delta E\) ? What is your reasoning? [Section 5.2]

Short Answer

Expert verified
(a) When compressing the air in the pump, work is being done on the system by the surroundings, so the sign of \(w\) is positive: \(w > 0\). (b) The pump's body gets warmer, indicating heat transfer is positive as heat is being absorbed by the system. Thus, the sign of \(q\) is positive: \(q > 0\). (c) The exact sign of ΔE cannot be determined without knowing the specific values of q and w. However, since the pump gets warmer during the compression process, it is expected that the change in internal energy (ΔE) would also be positive, i.e., \(ΔE > 0\).

Step by step solution

01

Determine the sign of work (w)

When compressing the air in the pump, the air undergoes a compression process, meaning work is being done on the system by the surroundings. According to the sign convention, work done on the system by the surroundings is considered positive. Thus, the sign of \(w\) is positive. Therefore, \(w > 0\).
02

Determine the sign of heat transfer (q)

The problem states that the pump's body gets warmer, indicating that heat is generated due to the compression process. This heat remains within the system (the pump and the compressed air). Therefore, the heat transfer is positive, meaning that heat is being absorbed by the system. Thus, the sign of \(q\) is positive. Therefore, \(q > 0\).
03

Determine the sign of change in internal energy (ΔE)

According to the first law of thermodynamics, the change in internal energy of a system is given by the equation: \[ΔE = q - w\] We have determined that both heat transfer (q) and work (w) are positive in this case. So, we cannot determine the exact sign of ΔE without knowing the specific values of q and w. However, since the pump gets warmer during the compression process, we can expect that the internal energy of the compressed air has increased as its temperature rises. Therefore, it is expected that the change in internal energy (ΔE) would also be positive, i.e., \(ΔE > 0\).

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Most popular questions from this chapter

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