Advising on Heat Pump Efficiency for 1500J at 280K

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SUMMARY

The discussion focuses on evaluating the efficiency of a heat pump that delivers 1500J to a room at 280K while consuming 50J of work per cycle, extracting heat from a surrounding environment at 270K. The key metric for assessing heat pump efficiency is the Coefficient of Performance (COP), calculated as COP = Q1/W, where Q1 is the heat delivered to the hot bath and W is the work input. Participants emphasize comparing the claimed COP with the theoretical maximum COP derived from the Carnot Cycle for the given temperatures to validate the heat pump's performance.

PREREQUISITES
  • Understanding of thermodynamic principles, specifically heat pumps
  • Familiarity with the Coefficient of Performance (COP) concept
  • Knowledge of the Carnot Cycle and its implications for efficiency
  • Basic mathematical skills for calculating efficiency ratios
NEXT STEPS
  • Research the Carnot Cycle and its efficiency calculations for heat pumps
  • Learn how to calculate the Coefficient of Performance (COP) for various heat pump systems
  • Explore real-world applications and limitations of heat pumps in different temperature environments
  • Investigate advanced thermodynamic cycles that improve heat pump efficiency
USEFUL FOR

Engineers, thermodynamics students, and HVAC professionals seeking to understand heat pump efficiency and performance evaluation methods.

captainjack2000
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Homework Statement


The question asks us to advise the company on a heat pump (and give reasons) which is claimed to deliver 1500J to a room at 280K by consuming 50J of work per cycle pumping heat from the surroundings at 270K.
I've drawn a diagram of the heat pump, taking heat Q2 from a bath of 270K up to an engine/refrigerator into which goes work W=50J, from which heat Q1 goes into hot bath of 280K. I am a bit confused about what to do next.
Is it that the efficiency of a heat pump is = Q1/W = Q1/ (Q1-Q2) = ?

thanks


Homework Equations





The Attempt at a Solution

 
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It's actually referred to as "coefficient of performance" or COP, but yes that is the right idea.

Compare the claimed COP with what you'd get for a Carnot Cycle heat pump operating at those temperatures, to determine whether this COP is possible.
 

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