An ideal gas is taken through a cyclic thermodynamic process through four steps. The amounts of heat involved in these steps are `Q_1=5960J, Q_2=-5585J, Q_3=-2980J and Q_4=3645J`, respectively. The corresponding quantities of work involved are `W_1=2200J, W_2=-825J, W_3=-1100J and W_4` respectively.
(1) Find the value of `W_4`.
(2) What is the efficiency of the cycle

Answer

A, B

Explanation

(i) The process is cyclic, therefore `DeltaU=0`
Now, `DeltaQ=DeltaU+DeltaW`
`rArrDeltaQ=DeltaW`
`rArrQ_1+Q_2+Q_3+Q_4=W_1+W_2+W_3+W_4`
`rArr5960-5585-2980+3645=2200-825-1100+W_4`
`rArrW_4=765J`
(ii) `Key Concept:eta=(work done)/(Heat supplied)`
`(W_1+W_2+W_3+W_4)/(Q_1+Q_4)`
`rArr=1040/9605=10.82%`