An ideal gas is made go to through a cyclic thermodynamics process in four steps. The `Q_(2)= 300J, Q_(3)= - 400J, Q_(4)= -100J` respectively. The corresponding works involved are `W_(1)= 300J, W_(2)= -100J, W_(3)= 100J and W_(4)`. What is the value of `W_(4)`?

Options

A. `100 J`
B. `500 J`
C. `-700 J`
D. `-400 J`

Answer

D

Explanation

According to first law of thermodyanmics,
`SigmadQ=SigmadU+SigmadW`
As the process is cycle, `SigmadU=0`
`:. SigmadW= SigmadQ`
`W_(1)+W_(2)+W_(3)+W_(4)= Q_(1)+Q_(2)+Q_(3)+Q_(4)`
`W_(4)= Q_(1)+Q_(2)Q_(3)+Q_(4)-(W_(1)+W_(2)+W_(3))`
`=100+300-400-100-(300-100+100)`
`= -100-300= -400J`