What are the Thermodynamic Considerations for an Air Conditioner Cooling a Room?

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SUMMARY

The discussion focuses on thermodynamic calculations related to an air conditioner operating at 800W with a coefficient of performance (C.o.P) of 2.80, in a room at 21°C and an outside temperature of 35°C. Key calculations include the rate of heat removal, heat discharge to the outside air, and total entropy changes for both the room and outside air over one hour. The equations utilized include the coefficient of performance formula and entropy change calculations, specifically \(\Delta S = Q/T\) and \(\Delta S = mc \ln(Th/Tc)\). Participants seek guidance on applying these equations to derive the necessary values.

PREREQUISITES
  • Understanding of thermodynamic principles, specifically heat transfer.
  • Familiarity with the coefficient of performance (C.o.P) in HVAC systems.
  • Knowledge of entropy and its calculations in thermodynamics.
  • Basic algebra and logarithmic functions for solving equations.
NEXT STEPS
  • Calculate the rate of heat removal using the formula \(Qc = W \times C.o.P\).
  • Perform a heat balance to determine the heat discharged to the outside air.
  • Study entropy change calculations in thermodynamic systems, focusing on \(\Delta S = Q/T\).
  • Explore the implications of net entropy change in closed systems and its significance in thermodynamics.
USEFUL FOR

Students and professionals in mechanical engineering, HVAC technicians, and anyone interested in the thermodynamic analysis of air conditioning systems.

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Homework Statement


An air conditioner operates on 800W of power and has a performance coefficient of 2.80 with a room temperature of 21oC, and an outside temperature of 35oC.
a) Calculate the rate of heat removal for this unit.
b) calculate the rate at which heat is discharged to the outside air.
c) calculate the total entropy change in the room if the air conditioner runs for 1 hour. Calculate the total entropy change in the outside air for the same time period.
d) What is the net change in entropy for the system(room+outside air)?


Homework Equations


\DeltaQ=cm\DeltaT
I think that that is the equation of heat lost
Coefficient of performance = Qcold, input/Winput
C.o.P=Qcold,input/(Qhot,output-Qcold,input)

The Attempt at a Solution



a) I'm not sure how to find the rate of heat which is removed

b) I'm not sure either

c) I know that Entropy=Q/T, and
\DeltaS=mcln(Th/Tc)
c is the specific heat, m is mass

but I'm not sure how to find the final temperature from what's given in the problem, or the mass...


d) once I know the answer to part C, its fairly self explanatory

Can someone guide in the right direction for solving this
 
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Using COP=Qc/W to get Qc will give you how much heat is removed from the space.

for part b) you just need to do a simple heat balance on the system. (Consider what quantities are going in and what are going out)
 

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