Problem 7 - Chemistry: The Central Science

Question

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]

Step-by-Step Solution

Answer

In the bicycle pump compression process, the sign of work (w) is positive, as work is being done on the system, while the sign of heat exchange (q) is also positive, as the system is gaining heat. According to the first law of thermodynamics, the change in internal energy (ΔE) is given by: \[ΔE = q + w\] Since both q and w are positive, ΔE is also positive. This makes sense physically, as compressing the air in the pump increases its internal energy, consistent with the observation that the pump gets warmer during compression.

Step 1: Determine the sign of w

When you compress the air in a bicycle pump, you are doing work on the system (the air in the pump). Since work is being done on the system, the sign of w (work) is positive.

Step 2: Determine the sign of q

As you compress the air in the pump, the temperature of the air increases due to the work done on it. This means the system is gaining heat. Thus, the sign of q (heat exchange) is positive.

Step 3: Determine the sign of ΔE

Now we need to determine the sign of the change in internal energy (ΔE). Recall the first law of thermodynamics, which states that: \[ΔE = q + w\] Since both q and w are positive (as determined in Steps 1 and 2), the overall change in internal energy, ΔE, will also be positive.

Step 4: Reasoning

The sign of ΔE being positive makes sense physically because as you compress the air in the pump, you are doing work on the air, which increases its internal energy. This is also consistent with the observation that the pump gets warmer upon compression.