Statement 1: For an ideal gas expanded reversibly from the same initial state to the same final pressure, the work done in the adiabatic process is smaller than in the isothermal process. Statement 2:

Question

Statement 1: For an ideal gas expanded reversibly from the same initial state to the same final pressure, the work done in the adiabatic process is smaller than in the isothermal process.

Statement 2: For the same final pressure, the final volume reached in the adiabatic process is larger than in the isothermal process.

TestHub · Accepted Answer

Take (P 1 ,V 1 )→ P 2 . Isothermal: V 2 iso =P 1 V 1 /P 2 . Adiabatic: V 2 ad =V 1 (P 1 /P 2 ) 1/γ , smaller since 1/γ<1 and P 1 /P 2 >1. So II is incorrect. The adiabatic path lies below the isotherm and ends at smaller volume, so the area under it, |w|=(P 1 V 1 -P 2 V 2 ad )/(γ-1) versus P 1 V 1 ln(P 1 /P 2 ), is smaller (check with P 1 /P 2 =2, γ=5/3: adiabatic |w|/P 1 V 1 =1.5 (1-2 -2/3 )≈0.555; isothermal ln 2≈0.693). I is correct. Answer (c).

Chemistry - Thermodynamics - I Question with Solution | TestHub

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