A sample of an ideal gas is taken through the cyclic-process `ABCA` shown in Fig. It rejects `50 J` of heat during the part `AB`, doens not absorb or reject the heat during `BC`, and accepts `70 J` of heat during `CA`. Forty joules of works is done on the gas during the part `BC`. The internla energies at `B` and `C`, respectively, will be

Options

A. `1450 J` and `1410 J`
B. `1550 J` and `1590 J`
C. `1450 J` and `1490 J`
D. `1550 J` and `1510 J`

Answer

C

Explanation

c. Along `AB`
`Delta Q = Delta U + Delta W = U_(B) - U_(A) + Delta W`
or `- 50 = U_(B) - U_(A) = - 1500`
or `U_(B) = 1450 J`
Along path `BC`
or `Delta Q = U_(C ) - U_(B) + Delta W`
or `0 = U_(C ) - U_(B) + Delta W = U_(C ) - U_(B) + (-40)`
or `0 = U_(C ) - 1450 - 40` or `U_(C ) = 1490 J`