Carnot Heat Engine to Carnot Heat Pump

Click For Summary
SUMMARY

The discussion centers on the Carnot heat engine operating at a high temperature (Th = 800°C) and a low temperature (Tc = 50°C), which drives a Carnot heat pump with reservoirs at Th' = 50°C and Tc' = 0°C. The user initially attempts to calculate the ratio of heat absorbed by the heat engine to that of the heat pump using the Carnot efficiency formulas, but encounters an infinite ratio due to the temperature scale used. The key takeaway is the importance of using the correct temperature scale when calculating these ratios, as improper scaling leads to erroneous conclusions.

PREREQUISITES
  • Carnot cycle principles
  • Thermodynamic temperature scale (Kelvin)
  • Heat engine and heat pump efficiency calculations
  • Understanding of heat transfer concepts
NEXT STEPS
  • Study the Carnot cycle and its applications in thermodynamics
  • Learn about the Kelvin temperature scale and its significance in thermodynamic calculations
  • Explore the efficiency equations for heat engines and heat pumps
  • Investigate common mistakes in thermodynamic calculations and how to avoid them
USEFUL FOR

Students and professionals in thermodynamics, mechanical engineers, and anyone involved in the study or application of heat engines and heat pumps.

keith river
Messages
14
Reaction score
0
We have a carnot engine with Th = 800 degrees Celsius, and Tc = 50 degrees Celsius.
This produces a work which is drives a carnot heat pump which has heat reservoirs at Th' = 50 degrees celsius and Tc' = 0 degress Celsius.
What is the ratio of heat absorbed by the Heat Engine to the heat absorbed by the heat pump.

I know the ratio from Qh/Qc for the heat engine would be Th/Tc but when I was planning on doing the same for a heat pump (Qh'/Qc') but It doesn't work out as the ratio would be infinite (divides by 0)
I was going to rearrange for Qh/Qc' as these are the heats absorbed by the heat engine and pump respectfully but this also would be infinite.
 
Physics news on Phys.org
keith river said:
We have a carnot engine with Th = 800 degrees Celsius, and Tc = 50 degrees Celsius.
This produces a work which is drives a carnot heat pump which has heat reservoirs at Th' = 50 degrees celsius and Tc' = 0 degress Celsius.
What is the ratio of heat absorbed by the Heat Engine to the heat absorbed by the heat pump.

I know the ratio from Qh/Qc for the heat engine would be Th/Tc but when I was planning on doing the same for a heat pump (Qh'/Qc') but It doesn't work out as the ratio would be infinite (divides by 0)
I was going to rearrange for Qh/Qc' as these are the heats absorbed by the heat engine and pump respectfully but this also would be infinite.
You are using the wrong scale for temperature.

AM
 
Thanks AM
I can't believe I never noticed that before. Such a simple problem.
 

Similar threads

Clausius' Theorem: Solving the Mystery of T ∑(dQi/Ti) =< 0
  • · Replies 5 ·
Replies
5
Views
2K
High School Heat pump as a heat engine that operates in reverse
  • · Replies 19 ·
Replies
19
Views
5K
Chemistry Work done by heat engine that uses exhaust from heat pump
  • · Replies 9 ·
Replies
9
Views
3K
Ammonia Rankine cycle heat engine calculation
  • · Replies 6 ·
Replies
6
Views
2K
Efficiency of Stirling heat engines
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Can Heat Engine Efficiency Be Related to Temperature?
  • · Replies 3 ·
Replies
3
Views
5K
High School Question regarding Heat Transfer in Carnot Engine
  • · Replies 1 ·
Replies
1
Views
2K
Carnot engine efficiency problem
  • · Replies 3 ·
Replies
3
Views
4K
High School Thermal physics, COP upper bound for heat driven heat pumps
  • · Replies 1 ·
Replies
1
Views
3K
Efficiency and Temperature in Heat Engine Cycles: Approaching Parts B, C, and D
  • · Replies 1 ·
Replies
1
Views
1K