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

In summary, the Carnot engine is a type of heat engine that uses hot and cold reservoirs with temperatures of 1684 K and 842 K, respectively. The input heat for the engine is |QH| and the work delivered is used to operate a Carnot heat pump, which removes heat from the 842-K reservoir and transfers it to a hot reservoir at temperature T`. The amount of heat removed from the 842-K reservoir is also |QH|. Using the equation |Q_c|/|Q_h|=T_c/T_h and rearranging to |W| = 1/2 |Q_h|, the temperature T` can be found to be 1684 K, but further clarification or guidance may
  • #1
frankwilson
3
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?
 
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  • #2
This was posted earlier. Please don't double post.

AM
 
  • #3
I'm really sorry, I am new to the forum and wasn't sure which category to post it in. Will not happen again.
 

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

What is a Carnot heat pump?

A Carnot heat pump is a theoretical device that uses thermodynamic cycles to transfer heat from a colder reservoir to a hotter one. It operates based on the principle of reversibility, meaning that it can theoretically achieve 100% efficiency.

How does a Carnot heat pump work?

A Carnot heat pump works by using a reversible thermodynamic cycle, which consists of two isothermal processes and two adiabatic processes. Heat is absorbed from the colder reservoir during the isothermal expansion process and then rejected to the hotter reservoir during the isothermal compression process. The adiabatic processes help maintain the temperature difference between the two reservoirs.

What is the equation for a Carnot heat pump?

The equation for a Carnot heat pump is |Q_c|/|Q_h| = T_c/T_h, where |Q_c| is the absolute value of the heat absorbed from the colder reservoir, |Q_h| is the absolute value of the heat rejected to the hotter reservoir, T_c is the temperature of the colder reservoir, and T_h is the temperature of the hotter reservoir.

What is the significance of the Carnot heat pump equation?

The Carnot heat pump equation is significant because it shows the maximum theoretical efficiency that a heat pump can achieve. It also helps in understanding the relationship between the temperature difference and the efficiency of a heat pump.

What are the limitations of a Carnot heat pump?

Some limitations of a Carnot heat pump include the assumption of ideal conditions and the requirement of a reversible thermodynamic cycle, which is not possible to achieve in real-world systems. Additionally, the efficiency of a Carnot heat pump decreases as the temperature difference between the two reservoirs increases.

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