Answer:
The minimum work per unit heat transfer will be 0.15.
Explanation:
We know the for a heat pump the coefficient of performance ([tex]C_{HP}[/tex]) is given by
[tex]C_{HP} = \dfrac{Q_{H}}{W_{in}}[/tex]
where, [tex]Q_{H}[/tex] is the magnitude of heat transfer between cyclic device and high-temperature medium at temperature [tex]T_{H}[/tex] and [tex]W_{in}[/tex] is the required input and is given by [tex]W_{in} = Q_{H} - Q_{L}[/tex], [tex]Q_{L}[/tex] being magnitude of heat transfer between cyclic device and low-temperature [tex]T_{L}[/tex]. Therefore, from above equation we can write,
[tex]&& \dfrac{Q_{H}}{W_{in}} = \dfrac{Q_{H}}{Q_{H} - Q_{L}} = \dfrac{1}{1 - \dfrac{Q_{L}}{Q_{H}}} = \dfrac{1}{1 - \dfrac{T_{L}}{T_{H}}}[/tex]
Given, [tex]T_{L} = 460 K[/tex] and [tex]T_{H} = 540 K[/tex]. So, the minimum work per unit heat transfer is given by
[tex]\dfrac{W_{in}}{Q_{H}} = \dfrac{T_{H} - T_{L}}{T_{H}} = \dfrac{540 - 460}{540} = 0.15[/tex]
