Answer
we know that ,
here ,
$Q_{out}$ = 250 kJ and beta = 1.8
(COP)beta = $Q_{in}$ /$W_{cycle}$ and also
$W_{cycle}$ = $Q_{out}$ - $Q_{in}$
(COP)beta = $Q_{in}$ /($Q_{out}$ - $Q_{in}$ )
so
$Q_{in}$ = beta($Q_{out}$ - $Q_{in}$) = $Q_{out}$( beta/(beta+1)) = 250 kJ(1.8/(1+1.8)) =161 kJ
$W_{cycle}$ = $Q_{in}$/beta = 161/1.8 = 89 kJ
Work Step by Step
we know that ,
here ,
$Q_{out}$ = 250 kJ and beta = 1.8
(COP)beta = $Q_{in}$ /$W_{cycle}$ and also
$W_{cycle}$ = $Q_{out}$ - $Q_{in}$
(COP)beta = $Q_{in}$ /($Q_{out}$ - $Q_{in}$ )
so
$Q_{in}$ = beta($Q_{out}$ - $Q_{in}$) = $Q_{out}$( beta/(beta+1)) = 250 kJ(1.8/(1+1.8)) =161 kJ
$W_{cycle}$ = $Q_{in}$/beta = 161/1.8 = 89 kJ
