Problem 7 - Chemistry The Central Science In Si Units

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

The sign of \( w \) is positive, the sign of \( q \) is zero, and \( \Delta E \) is positive, indicating an increase in internal energy.

Step 1: Understanding Work (w) in Compression

When you compress air in a bicycle pump, you are doing work on the system (the pump and the air). According to the convention, when work is done on a system, the work (w) is positive. Thus, for this process, the sign of \( w \) is positive.

Step 2: Analyzing Heat Transfer (q)

As you compress the air, the pump gets warmer, which indicates that heat is being generated due to work done. Since the system is not gaining heat from an external source but rather generating it internally, the sign of \( q \) is zero because there is no net heat exchange with surroundings.

Step 3: Determining Change in Energy (ΔE)

The change in internal energy \( \Delta E \) of a system is given by the equation \( \Delta E = q + w \). From the previous steps, we have \( w = + \) and \( q = 0 \). Substituting these values gives \( \Delta E = 0 + w = +w \). Thus, \( \Delta E \) is positive, meaning the internal energy of the system increases.

Key Concepts

Work

When you compress air in a bicycle pump, you are performing something called 'work' on the system. In thermodynamics, 'work' refers to energy transferred by a force over a distance. In our case, when you push the pump handle, you are applying a force over a distance to compress the air inside.

According to thermodynamic conventions, if work is done **on** the system (like compressing the air), then the work is considered positive. This is because energy is entering the system as work, meaning the system gains energy. Hence, when you use the pump, the sign of the work (denoted as \( w \)) is positive. This positive work contributes to increased pressure and temperature within the pump and its air.

Understanding this concept helps to explain why the pump gets warm — work is being added, raising the energy of the system which can manifest as heat.

Heat Transfer

Unlike work, 'heat transfer' refers to energy transfer due to a temperature difference between the system and its surroundings. In our bicycle pump example, the warmth you feel on the pump's body after compressing the air suggests heat is involved.

However, the pump's warmth is not due to heat entering from the outside environment. Instead, the rise in temperature results from the work done on the system, increasing its internal energy. Consequently, there is no heat exchange with the environment.

In thermodynamics, this scenario implies that \( q \), the heat transfer term, is zero. This means no net energy as heat is transferred into or out of the system, despite the rising temperature during compression.

Recognizing that \( q = 0 \) during compression helps us understand how certain processes can involve substantial temperature changes without heat transfer from the surroundings.

Internal Energy

The internal energy of a system, represented as \( \Delta E \), encompasses all the energy contained within the system. It includes kinetic energy, potential energy, and other microscopic energies related to temperature and molecular motion.

In thermodynamics, the change in internal energy (\({\Delta E}\)) is given by the equation:
\[ \Delta E = q + w \]

In the bicycle pump scenario, we've observed that \( q = 0 \) (no heat transfer) and \( w \) is positive (work done on the system). Substituting these values into the equation, we get \( \Delta E = +w \).

This positive \( \Delta E \) indicates the internal energy of the system has increased. This explains why the pump's body gets warmer — the internal energy growth from doing work is reflected as an increase in temperature.

Understanding the relationship between work, heat transfer, and internal energy helps demystify how energy changes occur in thermodynamic processes. It underscores the idea that energy can manifest in different forms within a system.