Question

Which of the following is not accompanied by an increase in the entropy of the system? (a) mixing of two gases at the same temperature and pressure, (b) mixing of ethanol and water, (c) discharging a battery, (d) expansion of a gas followed by compression to its original temperature, pressure, and volume.

Short answer

The process which is not accompanied by an increase in the entropy of the system is (d) expansion of a gas followed by compression to its original temperature, pressure, and volume.

Step-by-step solution

Analysis of option (a)

When two gases mix at the same temperature and pressure, the combined gases will have more potential configurations than the individual gases, increasing the system's randomness and thus the entropy. Therefore, answer (a) is accompanied by an increase in entropy.

Analysis of option (b)

A similar logic applies when discussing the mixing of ethanol and water. These molecules spread out among each other, increasing possible configurations and thus entropy. Therefore, answer (b) is also accompanied by an increase in entropy.

Analysis of option (c)

The discharging of a battery is a spontaneous process that increases entropy because it releases stored energy, spreading it out in a more disordered state. Therefore, answer (c) also accompanies an increase in entropy.

Analysis of option (d)

Expansion of a gas followed by compression to its original temperature, pressure, and volume is a cyclical process. In this process, the system returns to its original state, and overall, there is no net change in the randomness of the system. Therefore, unlike the other options, answer (d) does not cause an increase in the entropy of the system.

Key concepts

Entropy Increase

Entropy is a measure of disorder or randomness in a system. A system with higher entropy is more disordered and has more possible configurations. When a process occurs that increases the system's randomness, the entropy rises. In the context of thermodynamics, it's essential to understand how different actions like mixing substances or energy transformations can affect entropy. - **Mixing Processes**: When two substances like gases or liquids are mixed, they tend to spread out among each other. This spreading results in an increase in the number of possible configurations of molecules, thus raising entropy. - **Energy Changes**: When stored energy is released, as in the discharging of a battery, the energy disperses, increasing the disorder and thus increasing entropy. Overall, any process that leads to greater randomness in the system increases entropy. The curious thing about entropy is that it generally tends to increase in natural processes, leading to the second law of thermodynamics.

Gas Expansion and Compression

Gas expansion and compression are activities that directly involve changes in entropy, especially in a cyclical process. When a gas expands, it occupies a larger volume, allowing the molecules more space to spread out, which increases the system's entropy due to increased randomness. However, this can change significantly if the process is followed by a compression that returns the gas to its original state. - **Expansion**: Molecules become more spread out, increasing disorder, hence entropy. - **Compression**: If the gas is compressed back to its original volume, temperature, and pressure, the orderly state prior to expansion is restored. In a full cycle like the one described, where the gas returns to its initial state, the overall entropy change in the system can be zero. This is because even though entropy increases during expansion, it decreases during compression, balancing the changes out.

Spontaneous Process

A spontaneous process is one that occurs naturally without input of additional energy. These processes are often associated with an increase in entropy as they tend to move a system toward a state of greater disorder. - **Energy Release**: Spontaneous processes, such as the discharging of a battery, release energy. This energy disperses within the environment, leading to increased randomness and higher entropy. - **Natural Tendency**: Systems naturally evolve from states of lower probability and order to states of higher probability and disorder. This explains why spontaneous processes are often irreversible. Understanding spontaneous processes requires an appreciation of how they align with the second law of thermodynamics, which states that the total entropy of a closed system can never decrease over time.

Mixing of Substances

Mixing different substances is a classic example of an entropy-increasing process. When substances are mixed, like gases or liquids, their molecular interactions lead to new arrangements that increase the number of possible states for the system. - **Molecular Mixing**: When two gases or a liquid like ethanol with water mix, the molecules of each substance spread throughout the available space. This molecular spreading maximizes the randomness and increases entropy. - **Irreversibility**: Such mixing processes are generally irreversible because once mixed, the substances naturally spread out and achieve a state of equilibrium. Mixing leads to a more homogenous mixture as the substances become indistinguishable in terms of their initial concentrations, further illustrating the principle of increasing entropy through spreading and distribution.