Clausius Inequality The Clausius inequality establishes a connection between the spontaneity of a process and the change in its entropy. It states that in a...
Clausius Inequality
The Clausius inequality establishes a connection between the spontaneity of a process and the change in its entropy. It states that in any cyclic process, the total change in entropy must be non-negative. This means that the total amount of entropy that can be extracted from a closed system must be non-negative over time.
Key Points:
A cyclic process involves a loop in which the system returns to its initial state.
Entropy is a measure of the disorder or randomness of a system.
Clausius inequality ensures that the total entropy of a cyclic process remains non-negative.
It implies that it is impossible to achieve a net increase in entropy for a closed system over a cycle.
Examples:
In a cycle of expansion and compression of an ideal gas, the total entropy remains constant. This is because the gas undergoes a complete cycle, returning to its initial state, resulting in no net change in entropy.
In a heat engine operating in a cycle, the Clausius inequality is satisfied if the efficiency of the engine is less than 100%. This means that some energy is lost as waste during the cycle.
For a system undergoing a cyclic process, the Clausius inequality implies that the work done in the cycle must be zero, as any positive work done would be dissipated as heat