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]

Short answer

(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

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, \(w > 0\).

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, \(q > 0\).

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., \(ΔE > 0\).

Key concepts

Work done on a system

When thinking about work being done on a system in thermodynamics, remember that it reflects the interaction between the system and its surroundings. In the context of the bicycle pump scenario, work is done when you compress the air in the pump. This process involves applying a force that pushes the air particles closer together. As a result, energy is transferred into the system, typically raising its internal pressure.
According to thermodynamic conventions, the work done on a system by the surroundings is considered to have a positive sign. This is because energy is entering the system, potentially affecting its internal state.
In our bicycle pump example, when the surroundings—that's your hand pressing down on the pump handle—do work on the air inside, it's increasing the energy contained within that air. Thus, the sign of work (denoted as \( w \) in equations) in this compression process is positive, meaning \( w > 0 \).

• Work done on a system: positive sign \( (w > 0) \)
• Energy is transferred into the system, often affecting its internal conditions.

Heat transfer

Heat transfer is another crucial concept in understanding thermodynamic processes. It refers to the movement of thermal energy between the system and its surroundings.
During the compression of air in the bicycle pump, you might notice the pump getting hotter. This indicates that heat is being generated due to the work done on the system—a process known as adiabatic compression if no heat escapes.
The key idea here is that if the system absorbs heat, the sign of that heat transfer (denoted as \( q \) in the equation) is positive. In our case, the heat generated from compressing the air remains within the bicycle pump, signifying that the system absorbs the heat rather than letting it escape.
Consequently, the heat transfer for this process is positive, meaning \( q > 0 \).

• Heat transfer: positive sign \( (q > 0) \)
• The system absorbs thermal energy, increasing its internal energy.

Change in internal energy

In thermodynamics, the change in a system's internal energy reflects how the total energy within has altered due to work done and heat transfer. By using the first law of thermodynamics, the change in internal energy \( \Delta E \) can be calculated with the formula:
\[\Delta E = q - w\] This equation ties together both the heat transfer and work done on the system.
In the compression process of a bicycle pump, we've established that both \( q \) and \( w \) are positive. However, the specific value of \( \Delta E \) depends on the relative magnitudes of \( q \) and \( w \).
Without precise measurements, we can't perfectly determine their balance, but we know the pump's temperature rises. This suggests the system's internal energy has increased, indicating a positive \( \Delta E \).

• Change in internal energy \( (\Delta E > 0) \): total internal energy rises during compression.
• Relies on the relation between heat absorbed and work done on the system.