An ideal gas is expanded from ( p 1   ,   V 1   ,   T 1 )   to   ( p 2   …

An ideal gas is expanded from (p1 , V1 , T1) to (p2 , V2 , T2) under different conditions. The correct statement(s) among the following is(are)
  1. The work done on the gas is maximum when it is compressed irreversibly from ( p2 , V2) to (p1  , V1) against constant pressure p1
  2. If the expansion is carried out freely, it is simultaneously both isothermal as well as adiabatic
  3. The work done on the gas is less when it is expanded reversibly from V1 to V2 under adiabatic conditions as compared to that when expanded reversibly from V1 to V2 under isothermal conditions.
  4. The change in internal energy of the gas (i) zero, if it is expanded reversibly with T1= T2 , and (ii) positive, if it is expanded reversibly under adiabatic conditions with T1 ≠T2

Solution

(I)

 

(II) 

(III)  (i) ΔU=nCv ΔT=0 (isothermal hence ΔT=0)

(ii)   ΔU=q+w= -ve q=0, w<0

(IV)   q=0 (adiabatic), w=0 (free expansion)

ΔU=0  ⇒   ΔT=0 (isothermal)

Asked in: JEE Advanced 2017 (Paper 1)

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