An ideal gas is taken from state `1` to state `2` through optional path `A, B, C and D` as shown in the `PV` diagram. Let `Q, W and U` represent the heat supplied, work done and change in internal energy of the gas respectively.
Then,

Options

A. `Q_(A) - Q(D) = W_(A) - W(D)`
B. `Q_(B) - W(B) gt Q_(C) - W(C)`
C. `W_(A) lt W(B) lt W_(C) - W(D)`
D. `Q_(A) lt Q(B) lt Q_(C) - Q(D)`

Answer

A

Explanation

Work done by gas in all four process is positive and in order
`W_A gt W_B gt W_C gt W_D`
`implies ` c is false
The change in intial energy `U` is same for all process.
`:. Q_(A) = U +W_A` ..(1)
` Q_(B) = U +W_B` ..(2)
` Q_(C) = U +W_C` ..(3)
` Q_(4) = U +W_A` ..(4)
Hence `Q_(A) gtQ_B gt Q_C gtQ_D`
`implies ` (d) is false
From equation (1) and (4) ltbr. `Q_A - Q_C = W_B - W_C`
`implies` (b) is false.