Question

Two Carnot air conditioners, A and B, are removing heat from different rooms. The outside temperature is the same for both rooms, 314 K. The room serviced by unit A is kept at a temperature of 292 K, while the room serviced by unit B is kept at 298 K. The heat removed from either room is 4430 J. For both units, find (a), (b) the magnitude of the work required and (c), (d) the magnitude of the heat deposited outside for A and B conditioners respectively

Answer 1

(a) 333.77 J

(b) 237.85 J

(c) 4763.77 J

(d) 4667.85 J

Step-by-step explanation:

Temperature of source, TH = 314 K

Temperature of A, Tc = 292 K

Temperature of B, Tc' = 298 K

heat taken out, Qc = 4430 J

Let the heat deposited outside is QH and QH' by A and B respectively.

`(Q_H)/(Q_c)=(T_H)/(T_c)\\\\Q_H = (4430*314)/(292)=4763.77 J`

Now

`(Q_H')/(Q_c)=(T_H)/(T_c')\\\\Q_H' = (4430*314)/(298)=4667.85 J`

(a) Work done for A

W = QH - QC = 4763.77 - 4430 = 333.77 J

(b) Work done for B

W' = QH' - Qc = 4667.85 - 4430 = 237.85 J

(c) QH = 4763.77 J

(d) QH' = 4667.85 J