In the given figure an ideal gas changes its state from `A` to state `C` by two paths `ABC` and `AC`.

(i) Find the path along which work done is the least.
(ii) The internal energy of gas at `A` is `10J` and amount of heat supplied to change its state to `C` through the path `AC` is `200J`. Calculate the internal energy at `C`.
(iii) How much is the heat involved in the process `ABC` and `ADC`?

Answer

`AC , 170J, 10J`

Explanation

(i) `W_(AC) lt W_(ABC)` (Area under PV-graph gives work)
(ii) `U_(A) = 10J`
`Q_(AC) = 200J`
`DeltaW_(AC) = (1)/(2)xx (6-2) xx (15+5)= (4xx20)/(2) = 40J`
`implies Q = DeltaU + W implies 200 = (U_(C)-10) +40`
`implies U_(C) = 200+10-40= 210 -40 = 170J`
(iii) `Q_(AB) = DeltaU_(AB) + W_(AB) = (U_(B) - U_(A)) + W_(ArarrB)= (20-10) + 0 = 10J`