Work Done in Isothermal vs Adiabatic Expansion – Rankers Physics

Thermodynamics: Practice Problem & Solution

Assertion (A): Work done by a gas in isothermal expansion is more than the work done by the gas in the same expansion adiabatically. Reason (R): Temperature remains constant in isothermal expansion but not in adiabatic expansion.  
(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

Short Solution (Best for NEET):

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

Assertion (A) is true. For the same volume expansion, work done \(W = int P dV\). In isothermal expansion, \(P\) drops slower than in adiabatic expansion (due to heat supply), so the area under the \(P-V\) curve is greater for isothermal. Reason (R) is also true and explains why \(P\) behaves differently, leading to different work done.

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