Question

When a system is adiabatic, what can be said about the entropy change of the substance in the system?

Short answer

Answer: In an adiabatic process, the entropy change of the substance within the system is zero (∆S = 0). This indicates that an adiabatic process is an isentropic process, meaning the entropy remains constant.

Step-by-step solution

Entropic change definition

In thermodynamics, entropy (denoted as S) is a measure of the randomness or disorder in a system. Entropy is related to heat transfer (Q) and the temperature (T) of the system with the equation: \Delta S = \frac{\Delta Q}{T} Here, \Delta represents the change, \Delta S is the change in entropy, and \Delta Q is the change in heat transfer.

Adiabatic process characteristics

In an adiabatic process, no heat is exchanged between the system and the surroundings. Therefore, the change in heat transfer is zero (\Delta Q = 0), because there is no heat coming in or going out of the system.

Entropy change in an adiabatic process

Since \Delta Q = 0 and the entropy change (\Delta S) is given by the equation: \Delta S = \frac{\Delta Q}{T} Then, substituting \Delta Q = 0 in the equation, we get: \Delta S = \frac{0}{T} Which simplifies to: \Delta S = 0

Conclusion

In an adiabatic process, the entropy change of the substance within the system is zero (\Delta S = 0). This indicates that an adiabatic process is an isentropic process, which means that the entropy remains constant.

Key concepts

Entropy Change

Understanding entropy is crucial to grasp the behavior of systems in thermodynamics. Entropy, symbolized by the letter S, represents the degree of disorder or randomness within a system. The change in entropy, denoted as \( \Delta S \), is indicative of how the disorder of the system changes over a thermodynamic process.

Entropy change can be calculated using the formula \( \Delta S = \frac{\Delta Q}{T} \), where \( \Delta Q \) is the heat transfer to or from the system, and T is the absolute temperature. If a system receives heat, its disorder increases, leading to a positive entropy change. Conversely, if a system loses heat, disorder typically decreases, and the entropy change is negative. In a perfectly insulated system where no heat is exchanged with the surroundings, like an adiabatic process, the entropy change is zero. This fundamental understanding is key to solving problems related to entropy in thermodynamics.

Thermodynamic Processes

A thermodynamic process refers to the path of a system’s state change due to energy transfer as work or heat. There are various types of thermodynamic processes distinguished by their distinct characteristics:

• Isobaric: The process occurs at constant pressure.
• Isochoric: The process happens at constant volume.
• Isothermal: The process unfolds at constant temperature.
• Adiabatic: No heat is exchanged with the surroundings.

Each type of process brings about different changes in variables such as pressure, volume, temperature, and entropy. Understanding these differences is essential to analyzing how a system evolves and predicting the outcome of thermodynamic operations.

Isentropic Process

An isentropic process is a special case in thermodynamics where the entropy of the system remains constant throughout the process. It is an idealization that often serves as a model for real processes, given that no real process is perfectly isentropic due to the presence of irreversibilities such as friction and heat loss.

Diving deeper, during an isentropic process, energy transfer is solely due to work done on or by the system, with no heat added to or removed from it (an adiabatic process). This implies the system is perfectly insulated so that the total entropy stays unchanged (\( \Delta S = 0 \)). Isentropic processes are significant in understanding the efficiency and behavior of various thermodynamic cycles, such as the Carnot cycle, which is used to determine the maximum possible efficiency of heat engines.