Answer:
Explanation:
The thermal efficiency of a Power cycle [tex]\eta = \dfrac{Q_H -Q_c}{Q_H}[/tex]
where;
[tex]\eta = 50\% = 0.5[/tex]
[tex]Q_H = Heat \ flow \ from \ higher \ temperature[/tex]
[tex]Q_c = Heat \ flow \ from \ lower \ temperature[/tex]
[tex]0.5 = \dfrac{Q_H -Q_c}{Q_H}[/tex]
[tex]0.5 Q_H = Q_H - Q_c[/tex] --- (1)
[tex]Q_c = 0.5 Q_H[/tex] ---- (2)
The coefficient of performance is:
[tex]COP_R = \dfrac{Q_c}{Q_H -Q_c}[/tex]
let replace the value of [tex]Q_c = 0.5 Q_H[/tex] in the above equation then;
[tex]COP_R = \dfrac{0.5Q_H}{Q_H -0.5 Q_H}[/tex]
[tex]COP_R = \dfrac{0.5Q_H}{0.5 Q_H}[/tex]
[tex]COP_R = 1[/tex]
The
On the other hand, the heat pump
[tex]COP_{HP} = \dfrac{Q_H}{Q_H -Q_c}[/tex]
By replacing equation (1) into the above equation; we have:
[tex]COP_{HP} = \dfrac{Q_H}{0.5Q_{H}}[/tex]
[tex]COP_{HP} = \dfrac{1}{0.5}[/tex]
[tex]COP_{HP} =2[/tex]
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