Carnot Heat Pumps: Solving |Q_c|/|Q_h|=T_c/T_h Equation

  • Thread starter Thread starter frankwilson
  • Start date Start date
  • Tags Tags
    Carnot Heat Pumps
Click For Summary
SUMMARY

The discussion centers on the application of the Carnot heat pump and the relationship between the heat absorbed and rejected, defined by the equation |Q_c|/|Q_h|=T_c/T_h. The temperatures of the hot and cold reservoirs are given as 1684 K and 842 K, respectively. The work delivered by the Carnot engine is utilized to operate the heat pump, which transfers heat from the cold reservoir to a hot reservoir at temperature T`. The user derived the equation |W| = 1/2 |Q_h| but expressed uncertainty about the final temperature T`, which was calculated to be 1684 K.

PREREQUISITES
  • Understanding of Carnot cycle principles
  • Familiarity with thermodynamic equations
  • Knowledge of heat transfer concepts
  • Basic algebra for rearranging equations
NEXT STEPS
  • Study the Carnot cycle and its efficiency calculations
  • Learn about heat pump operation and performance metrics
  • Explore thermodynamic properties of substances at various temperatures
  • Investigate the implications of the second law of thermodynamics on heat engines
USEFUL FOR

Students and professionals in thermodynamics, mechanical engineers, and anyone interested in the principles of heat engines and heat pumps.

frankwilson
Messages
3
Reaction score
0
A Carnot engine uses hot and cold reservoirs that have temperatures of 1684 and 842 K, respectively. The input heat for this engine is |QH|. The work delivered by the engine is used to operate a Carnot heat pump. The pump removes heat from the 842-K reservoir and puts it into a hot reservoir at a temperature T`. The amount of heat removed from the 842-K reservoir is also |QH|. Find the temperature T`.


|Q_c|/|Q_h|=T_c/T_h
|Q_h|=|W| + |Q_c|


I'm having trouble visualizing this problem. Are there two separate engines? Doing a little rearranging, I was able to get down to |W| = 1/2 |Q_h|. I figure that since there are no values for either heat value or work that they cancel out. I'm just not sure how to proceed. I worked it one way and got my final T` to be 1684 K, but I don't feel too confident about it. Anyone out there know where I should start or if I'm even on the right track?
 
Physics news on Phys.org
This was posted earlier. Please don't double post.

AM
 
I'm really sorry, I am new to the forum and wasn't sure which category to post it in. Will not happen again.
 

Similar threads

Carnot Heat Pump: Solving |Q_c|/|Q_h|=T_c/T_h
  • · Replies 3 ·
Replies
3
Views
5K
Engine working between multiple temperature baths worse than Carnot
  • · Replies 1 ·
Replies
1
Views
1K
Efficiency of Stirling Cycle - Is it the same as the Carnot Engine?
  • · Replies 14 ·
Replies
14
Views
2K
High School Heat pump as a heat engine that operates in reverse
  • · Replies 19 ·
Replies
19
Views
5K
Net efficiency of a cascaded Carnot Engine and Fridge
  • · Replies 1 ·
Replies
1
Views
2K
I don't know how I got "mysterious energy" in a Carnot heat pump
  • · Replies 4 ·
Replies
4
Views
1K
What is the efficiency of a Carnot engine and the effectiveness of a heat pump?
  • · Replies 1 ·
Replies
1
Views
3K
Compute work in Carnot Refrigerator
  • · Replies 3 ·
Replies
3
Views
3K
Carnot Heat Engine: Solve for Heat Expelled to Cold Res.
  • · Replies 2 ·
Replies
2
Views
5K
High School Question regarding Heat Transfer in Carnot Engine
  • · Replies 1 ·
Replies
1
Views
2K