Work Air Conditioner Must Do To Keep Room Constant Temperature

AI Thread Summary
To maintain a room temperature of 27°C with external conditions at 42°C and an incoming heat of 2,000 Cal/s, the coefficient of performance (COP) is calculated as 20.01. The minimum work required by the air conditioner is derived using the formula Win = Qout/(1 + COP), resulting in a value of approximately 95.15 Cal/s or 398.1 J/s. It's important to ensure the correct interpretation of the output heat flow in the context of refrigeration systems. Additionally, the temperature conversion should be noted, as 0°C equals 273K. The calculations appear to be correct based on the provided equations.
trevor51590
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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 = Tc/(Th-Tc)
Win = Qout/(1+COP)

The Attempt at a Solution


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

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

W=95.15 Cal s-1 or 398.1 J s-1
Look okay?
 
Last edited:
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trevor51590 said:

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 = Tc/(Th-Tc)
Win = Qout/(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
 
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