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) =- 2989J` and `Q_(4) = 3645J` respectively. The corresponding works involved are `W_(1) = 2200J, W_(2) =- 825J, W_(3) =- 1100J` and `W_(4)` respectively.
(i) Find the value of `W_(4)`.
(ii) What is the efficiency of the cycle?

Answer

(i)`765 J (ii) 10.82 %`

Explanation

(i) For a cyclic process `Q_(1) + Q_(2) + Q_(3) + Q_(4) = W_(1) + W_(2) + W_(3) + W_(4)`
`implies W_(4) = Q_(1) + Q_(2) + Q_(3) + Q_(4) - W_(1) - W_(2) - W_(3)`
=`5960-5585-2980+3645-2200+825+1100`
=`765J`
(ii) `eta = (W_("net"))/(Q_("given")) = ( W_(1) + W_(2) + W_(3) + W_(4))/(Q_(1) + Q_(4))`
=`(220-825-1100+765)/(5960+3645) = 0.1082`