Consider a process in which an ideal gas changes from state 1 to state 2 in such a way that its temperature changes from 300 K to 200 K. (a) Does the temperature change depend on whether the process is reversible or irreversible?

Verified step by step guidance

1. insert step 1> Understand that temperature is a state function, which means it depends only on the initial and final states of the system, not on the path taken to get from one to the other.
2. insert step 2> Recognize that in this problem, the temperature change is from 300 K to 200 K, which are the initial and final states.
3. insert step 3> Since temperature is a state function, the change in temperature (\( \Delta T \)) is the same regardless of whether the process is reversible or irreversible.
4. insert step 4> Conclude that the temperature change does not depend on the nature of the process (reversible or irreversible).
5. insert step 5> Reiterate that the key concept here is the state function property of temperature, which ensures that \( \Delta T = T_{final} - T_{initial} \) is path-independent.

Key Concepts

Ideal Gas Law

The Ideal Gas Law describes the relationship between pressure, volume, temperature, and the number of moles of an ideal gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. Understanding this law is crucial for analyzing gas behavior during state changes.

Reversible vs. Irreversible Processes

Reversible processes are idealized processes that can be reversed without any net change in the system or surroundings, while irreversible processes cannot return to their original state without external work. The distinction affects how energy is transferred and how temperature changes occur, but the temperature change itself is a state function and does not depend on the path taken.

State Functions

State functions are properties that depend only on the current state of a system, not on the path taken to reach that state. Examples include temperature, pressure, and volume. In the context of the question, the change in temperature from 300 K to 200 K is a state function, meaning it remains the same regardless of whether the process is reversible or irreversible.