Work Air Conditioner Must Do To Keep Room Constant Temperature

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SUMMARY

The discussion focuses on calculating the minimum work required by an air conditioner to maintain a room temperature of 27°C when the external temperature is 42°C and the heat influx is 2,000 Cal/s. The Coefficient of Performance (COP) is calculated using the formula COP = Tc/(Th-Tc), yielding a value of 20.01. The work input (Win) is determined using the equation Win = Qout/(1+COP), resulting in a minimum work of 95.15 Cal/s or 398.1 J/s. The calculations are confirmed to be accurate with the correct application of thermodynamic principles.

PREREQUISITES
  • Understanding of thermodynamics, specifically the concepts of heat transfer and work.
  • Familiarity with the Coefficient of Performance (COP) in refrigeration cycles.
  • Knowledge of unit conversions between calories and joules.
  • Basic algebra for manipulating equations and solving for variables.
NEXT STEPS
  • Study the principles of thermodynamics related to refrigeration cycles.
  • Learn about the implications of COP in different cooling systems.
  • Explore advanced calculations involving heat exchangers and energy efficiency.
  • Investigate the impact of varying external temperatures on air conditioning performance.
USEFUL FOR

This discussion is beneficial for students studying thermodynamics, HVAC engineers, and anyone involved in designing or optimizing air conditioning systems.

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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