In the given an ideal gas can change its state from `A` to `C` by two paths `ABC` or `AC`. Then

Options

A. If the internal energy of gas `'A'` is `10J` and the amount of heat supplied in path `AC` is `200J`, then the internal energy of gas at `'C'` is `150J`
B. If the internal energyof gas at `'A'` is `10J` and the amount of heat supplied in path `AC` is `200J`, then the internal energy of gas at `'C'`is `75J`
C. If the internal energy of gas a state `B` is `20J`. Then the amount heat supplied to the gas to go from `A` to `B` may be 5 Joule.
D. If the internal energy of gas at state `B` is `20J`. Then the amount of heat supplied to the gas to go from `A` and `B` must be 10 Joule

Answer

A, D

Explanation

In path `AtoC`
`dW=4xx10+1/2xx10xx4+20=60J`
`dQ=dU+dW`
`200=U_(c)-U_(A)+60`
`U_(c)=U_(c)-U_(A)+60`
`U_(c)=140+U_(A)=140+10=150J`
In path `AtoB`
`Q_(AB)=U_(B)-U_(A)`
`=U_(B)(1-(U_(A))/(U_(B)))=U_(B)(1-(T_(A))/(T_(B)))`
`=20 (1- 1/2)=10` Joule