Solution Found!
Refrigeration and Heat Pump Cycle ApplicationsA reversible
Chapter 5, Problem 44P(choose chapter or problem)
A reversible refrigeration cycle operates between cold and hot reservoirs at temperatures \(T_{\mathrm{C}}\) and \(T_{\mathrm{H}}\), respectively.
(a) If the coefficient of performance is 3.5 and \(T_{\mathrm{H}}=80^{\circ} \mathrm{F}\), determine \(T_{\mathrm{C}}\), in \({ }^{\circ} \mathrm{F}\).
(b) If \(T_{\mathrm{C}}=-30^{\circ} \mathrm{C}\) and \(T_{\mathrm{H}}=30^{\circ} \mathrm{C}\), determine the coefficient of performance.
(c) If \(Q_{\mathrm{C}}=500 \mathrm{Btu}, Q_{\mathrm{H}}=800 \mathrm{\ Btu}\), and \(T_{\mathrm{C}}=20^{\circ} \mathrm{F}\), determine \(T_{\mathrm{H}}\), in \({ }^{\circ} \mathrm{F}\).
(d) If \(T_{\mathrm{C}}=30^{\circ} \mathrm{F}\) and \(T_{\mathrm{H}}=100^{\circ} \mathrm{F}\), determine the coefficient of performance.
(e) If the coefficient of performance is 8.9 and \(T_{\mathrm{C}}=-5^{\circ} \mathrm{C}\), find \(T_{\mathrm{H}}\), in \({ }^{\circ} \mathrm{C}\).
Questions & Answers
QUESTION:
A reversible refrigeration cycle operates between cold and hot reservoirs at temperatures \(T_{\mathrm{C}}\) and \(T_{\mathrm{H}}\), respectively.
(a) If the coefficient of performance is 3.5 and \(T_{\mathrm{H}}=80^{\circ} \mathrm{F}\), determine \(T_{\mathrm{C}}\), in \({ }^{\circ} \mathrm{F}\).
(b) If \(T_{\mathrm{C}}=-30^{\circ} \mathrm{C}\) and \(T_{\mathrm{H}}=30^{\circ} \mathrm{C}\), determine the coefficient of performance.
(c) If \(Q_{\mathrm{C}}=500 \mathrm{Btu}, Q_{\mathrm{H}}=800 \mathrm{\ Btu}\), and \(T_{\mathrm{C}}=20^{\circ} \mathrm{F}\), determine \(T_{\mathrm{H}}\), in \({ }^{\circ} \mathrm{F}\).
(d) If \(T_{\mathrm{C}}=30^{\circ} \mathrm{F}\) and \(T_{\mathrm{H}}=100^{\circ} \mathrm{F}\), determine the coefficient of performance.
(e) If the coefficient of performance is 8.9 and \(T_{\mathrm{C}}=-5^{\circ} \mathrm{C}\), find \(T_{\mathrm{H}}\), in \({ }^{\circ} \mathrm{C}\).
ANSWER:Solution 44P:
Step 1 of 5:-
All the cycles are reversible and we need to find the various parameters as per the question.
a)
The coefficient of performance is given as: .
The temperature of the hot reservoir is: .
We know the maximum coefficient of performance is:
-------------------(1)
As, these are reversible cycles,
So, equation (1) can be written as,
So, the temperature of the cold reservoir is: .