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

(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`