Two Carnot air conditioners, A and B, are removing heat from different rooms. Th
ID: 1306123 • Letter: T
Question
Two Carnot air conditioners, A and B, are removing heat from different rooms. The outside temperature is the same for both rooms, 315.0 K. The room serviced by unit A is kept at a temperature of 283.0 K, while the room serviced by unit B is kept at 302.0 K. The heat removed from either room is 4499 J. (a) Find the magnitude of the work required for air conditioner A.
(b) Find the magnitude of the work required for air conditioner B.
(c) Find the magnitude of the heat deposited outside for air conditioner A.
(d) Find the magnitude of the heat deposited outside for air conditioner B.
Explanation / Answer
The coefficient of performance for an heat pump in a cooling application is defined as amount of heat extracted from cold reservoir to work done to run the pump[1]:
COP = Q_c/W
=>
W = Q_c/COP
For an ideal Carnot heat pump it takes its maximum value of:
T_c /( T_h - T_c)
For your two pumps
COP_A = 283K/(315K - 283K) = 8.84375
COP_A = 302K/(315K - 302K) = 23.2307
(a)
W_A = Q_c/COP_A = 4499J / 8.84375 = 508.72J
(b)
W_B = Q_c/COP_B = 4499J / 23.23 = 193.67J
(c)
Q_hA = W_A + Q_c = 508.72J + 4499J = 5007.72J
(c)
Q_hB = W_B + Q_c = 193.67J + 4499J = 4692.67J
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.