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.
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:
Concept: Work done is area under P-V curve. Isothermal vs. Adiabatic expansion.
Formula: \( W = \int P dV \). Isothermal: \( PV = \text{constant} \). Adiabatic: \( PV^{\gamma} = \text{constant} \), where \( \gamma > 1 \).
Solution: During expansion from the same initial state to the same final volume, the pressure in isothermal process drops slower than in adiabatic process, leading to more work done. Temperature remains constant in isothermal and changes in adiabatic.
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