Adiabatic Expansion and Entropy – Rankers Physics

Thermodynamics: Practice Problem & Solution

Assertion (A): During adiabatic expansion of an ideal gas, temperature falls but entropy remains constant. Reason (R): During adiabatic expansion, work is done by the gas using a part of internal energy and no heat exchange takes place the system and the surrounding.  
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Thermodynamics. Understanding the underlying formula is key to arriving at the correct answer below:

During adiabatic expansion, \(Q=0\). The gas does work by using its internal energy, causing temperature to fall. For a reversible adiabatic process, entropy \(\Delta S=0\). (A) is true. (R) correctly explains the energy changes (no heat exchange, internal energy conversion to work) that lead to temperature drop and, for reversible processes, constant entropy. Both are true and (R) is the correct explanation of (A).

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