# Example Problem with Complete Solution

7A-1 : Process Paths and Cyclic Integrals 4 pts
Consider the cycle made of path A followed by path B shown below.

The following integrals have been evaluated.

Is this cycle reversible, irreversible or impossible?

Read : This is a straightforward application of the Clausius Inequality to a thermodynamic cycle interacting with two thermal reservoirs.
Diagram: See the problem statement.
Given: -24.7 kJ/K 41.3 kJ/K
Find: Is this cycle reversible, irreversible or impossible?
Assumptions: None.
Equations / Data / Solve:
The Clausius Inequality is: Eqn 1
If the cyclic integral is … ... positive, the cycle is impossible
... negative, the cycle is irreversible
... zero, the cycle is reversible
Since the cycle is made up of two steps, A & B, we can expand Eqn 1 as follows:
Eqn 2
Now, we can plug in values from the problem statement. 16.6 kJ/K
Because the cyclic integral is greater than zero, the cycle is impossible.
Verify: None.
Answers : Because the cyclic integral is greater than zero, the cycle is impossible.