How Does Temperature Difference Affect Air Conditioning Costs?

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SUMMARY

The discussion focuses on the relationship between temperature difference and air conditioning costs, specifically under conditions where heat enters a building primarily through conduction. It establishes that the cost of air conditioning is roughly proportional to the square of the temperature difference (Th - Tc). Key concepts include the Coefficient of Performance (COP) and its relation to work input and heat flow. Participants emphasize the importance of understanding how these factors interrelate to determine electricity costs associated with air conditioning.

PREREQUISITES
  • Understanding of Coefficient of Performance (COP) in thermodynamics
  • Basic principles of heat transfer, particularly conduction
  • Knowledge of electrical work input and its cost implications
  • Familiarity with temperature difference calculations in HVAC systems
NEXT STEPS
  • Research the ideal Coefficient of Performance (COP) for various air conditioning systems
  • Study the principles of heat transfer, focusing on conduction and its impact on HVAC efficiency
  • Examine the relationship between electricity costs and work input in air conditioning systems
  • Explore mathematical models that relate temperature differences to energy consumption in HVAC applications
USEFUL FOR

This discussion is beneficial for HVAC engineers, energy efficiency analysts, and anyone involved in the design or optimization of air conditioning systems, particularly in understanding cost implications related to temperature differences.

tralblaz
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Homework Statement



Under many conditions, the rate at which heat enters as air conditioned building on a hot summer day is proportional to the difference in the temperature between the inside and outside, Th-Tc. (If the heat enters entirley by conduction,this statement will certainly be true. Radiation from the direct sunlight would be an exception.) Show that, under these condtions, the cost of air condtioning should be roughly proportional to the square of the temperature difference.

Homework Equations


use what is known about COP (coefficient of performance)

COP=Q/W

The Attempt at a Solution


I am thoroughly lost in how to approach this problem. I know that the COP is involved, but I have no idea where or how to start.

Could someone please get me started? Thanks
 
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these are give away hints... but anyway.

1. consider the ideal COP, what is its relation to the temperature difference?

2. consider the work input (relating to cost of electricity) and its relationship between COP.

3. consider heat entering the house... if the air conditioner is "combating" this heat flow, how much heat must it take out (in relation to difference of temperature)?

4. relate 1, 2 and 3. So, what is cost of electricity proportional to?
 

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