Two moles of helium gas are taken along the path `ABCD` (as shown in Fig.) The work done by the gas is

Options

A. `2000 R(1+"in"(4)/(3))`
B. `500 R(3 + "in" 4)`
C. `500 R(2 + "In"(16)/(9))`
D. `1000 R(1 + "In"(16)/(9))`

Answer

C

Explanation

`A rarr B` is an isobaric process
`so, DeltaW_(AB) = nRDeltaT = 2 xx R xx (750-250)=1000R`
`B rarr C` is an isochoric process
`:. DeltaW_(BC)=0` and `C rarr D` is an isothermal process,
`DeltaW_(CD)=nRT 1n ((V_f)/(V_i))`
`=2xxRxx1000 1n(20/15)=2000 R 1n(4//3)`
Total work done `Delta W = sigmaDeltaW_(AB)`.