Work Air Conditioner Must Do To Keep Room Constant Temperature

[trevor51590]

Homework Statement

If a room is at 27C and the surroundings at 42C, and the heat into the room is 2,000 Cal s^-1. What is the minimum work the air conditioner must do to keep the room at 27C?

Homework Equations

COP = T_c/(T_h-T_c)
W_in = Q_out/(1+COP)

The Attempt at a Solution

COP = (300.15/(315.15-300.15)
COP = 20.01

W_in = 2,000 Cal s^-1/(1+20.11)

W=95.15 Cal s^-1 or 398.1 J s^-1
Look okay?

 

[Andrew Mason]

Homework Statement

If a room is at 27C and the surroundings at 42C, and the heat into the room is 2,000 Cal s^-1. What is the minimum work the air conditioner must do to keep the room at 27C?

Homework Equations

COP = T_c/(T_h-T_c)
W_in = Q_out/(1+COP)

You may want to check your expression for W. For a refrigerator output is the heat flow transferred from the cold reservoir, Qc, so COP = output/input = Qc/W. Also, use 0C = 273K.

AM