Question

If a gas at constant temperature and pressure expands, then its (a) internal energy decreases (b) entropy increases and then decreases (c) internal energy increases (d) internal energy remains constant

Short answer

The correct answer is (d): the internal energy remains constant.

Step-by-step solution

Understanding the Properties

When a gas expands at constant temperature (isothermal process), the internal energy of the gas, which is dependent on temperature, remains unchanged if we assume an ideal gas.

Evaluating Internal Energy

Since the temperature is constant and we are assuming ideal behavior, there is no change in internal energy during expansion. This rules out options (a) and (c) as they involve changes in internal energy.

Considering Entropy

In an isothermal expansion, the entropy of the gas increases as it occupies a greater volume. There is no immediate reason for the entropy to decrease after increasing, so option (b) is unlikely.

Selecting the Correct Answer

Based on the understanding that internal energy remains constant during isothermal expansion of an ideal gas, the best answer is option (d): the internal energy remains constant.

Key concepts

Isothermal Process

An isothermal process is a thermodynamic transformation that occurs at a constant temperature. This means that during an isothermal process, a system can exchange heat with its surroundings to ensure that the temperature remains unchanged. In the context of gases, an important implication of an isothermal process is the behavior of internal energy.

• For ideal gases, the internal energy is solely a function of temperature.
• During an isothermal expansion, no net change in internal energy occurs because the temperature is constant. This is key to understanding the behavior of ideal gases.
• Energy added during an isothermal process goes to do work on the surroundings rather than changing the internal energy.

This means any heat input into the system is fully used for work and maintaining temperature, establishing a consistent energy balance.

Internal Energy

Internal energy is the total energy contained within a system. In thermodynamic terms, it is the sum of all kinetic and potential energies of the particles within the system. The internal energy of an ideal gas depends solely on its temperature; hence any change in temperature results in a change in internal energy.

• During an isothermal process, the temperature of the system remains constant.
• For ideal gases, as the internal energy depends only on temperature, it remains unchanged during an isothermal expansion.
• The lack of change in internal energy means that all energy transfers are used to perform work on the surroundings.

Understanding these points helps reason why certain exercises prioritize temperature constancy in analyzing gas behavior.

Entropy

Entropy is a measurement of disorder or randomness within a system. It is also a way to describe inaccessible energy within a system that cannot be used to do work. When considering isothermal processes, entropy marks an interesting transformation.

• In an isothermal expansion, the volume the gas occupies increases.
• This leads to an increase in entropy because the gas particles have more space and become more disordered.
• Since entropy measures the system's randomness, larger volumes result in higher entropy.

It’s important to note that in an isothermal expansion, entropy does not decrease after increasing; it increases as long as the volume increases, thereby enhancing our understanding of thermodynamic principles.