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

Options

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

Answer

A

Explanation

a. `A rarr B` is isobaric process,
`V prop T`
so, `Delta W_(AB) = nR Delta T = 2 xx R xx (750 - 250) = 1000 R`
`B rarr C` is an isochoric process
`:. Delta W_(BC) = 0` and
`C rarr D` is an isothermal process
`Delta W_(CD) = nRT 1n ((V_(f))/(V_(i)))`
` = 2 xx R xx 1000 1n ((20)/(15)) = 2000 1n ((4)/(3))`
Total work done, `Delta W = Delta W_(AB) + Delta W_(BC) + Delta W_(CD)`