Answer:
a) [tex]T_{L} = 273.378\,K\,(0.228\,^{\textdegree}C)[/tex], b) [tex]\dot Q_{H} = 26.875\,kW[/tex]
Explanation:
a) The Coefficient of Performance of the Carnot Heat Pump is:
[tex]COP_{HP} = \frac{T_{H}}{T_{H}-T_{L}}[/tex]
After some algebraic handling, the temperature of the cold reservoir is determined:
[tex]T_{H}-T_{L} = \frac{T_{H}}{COP_{HP}}[/tex]
[tex]T_{L} = T_{H}\cdot \left(1-\frac{1}{COP_{HP}} \right)[/tex]
[tex]T_{L} = (297.15\,K)\cdot \left(1-\frac{1}{12.5}\right)[/tex]
[tex]T_{L} = 273.378\,K\,(0.228\,^{\textdegree}C)[/tex]
b) The heating load provided by the heat pump is:
[tex]\dot Q_{H} = COP_{HP}\cdot \dot W[/tex]
[tex]\dot Q_{H} = (12.5)\cdot (2.15\,kW)[/tex]
[tex]\dot Q_{H} = 26.875\,kW[/tex]
