Carnot Heat Engine: Solve for Heat Expelled to Cold Res.

In summary, a Carnot engine operating between a hot reservoir at 63°C and a cold reservoir at -14°C absorbs 590 J of heat in 25 minutes. To calculate the amount of heat expelled to the cold reservoir, we use the equation Q_H/Q_C = T_H/T_C and solve for Q_C, which gives us a value of 504 J. However, it is important to note that the correct temperature for the cold reservoir is -14°C, which corresponds to 287 K. Taking this into account, the correct answer is 504 J.
  • #1
tehjojo
2
0

Homework Statement



Consider a Carnot engine that operates between a hot reservoir at 63°C and a cold reservoir at -14°C. In running 25 minutes, this engine absorbs 590 J of heat from the hot reservoir.

How much heat does it expel to the cold reservoir?

Homework Equations


[tex]Q_H/Q_C = T_H/T_C[/tex]

The Attempt at a Solution


[tex]T_H = 336k[/tex]
[tex]T_C = 287k[/tex]
[tex]Q_H/Q_C = T_H/T_C \longrightarrow 590/Q_C = 336/287[/tex]
Solving for [tex]Q_C[/tex] I get 504 J, however, this is not the correct answer. What am I missing?
 
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  • #2
Are you sure Tc= 287 K? The cold reservoir is at -14 C
 
  • #3
Wow. It happened that on the site my homework is on, the negative sign and the number were on different lines, so I totally missed it. Thank you very much.
 

Related to Carnot Heat Engine: Solve for Heat Expelled to Cold Res.

1. What is a Carnot Heat Engine?

A Carnot Heat Engine is a theoretical engine that operates on the Carnot cycle, which is a reversible cycle of four thermodynamic processes. It is used to model the most efficient way of converting heat into work.

2. How does a Carnot Heat Engine work?

A Carnot Heat Engine works by taking in heat energy from a hot reservoir, converting some of it into work, and then releasing the remaining heat energy into a cold reservoir. This process is repeated in a continuous cycle.

3. How do you calculate the heat expelled to the cold reservoir in a Carnot Heat Engine?

The heat expelled to the cold reservoir in a Carnot Heat Engine can be calculated using the formula Qc = Qh - W, where Qc is the heat expelled, Qh is the heat taken in from the hot reservoir, and W is the work output.

4. What factors affect the efficiency of a Carnot Heat Engine?

The efficiency of a Carnot Heat Engine is affected by the temperature difference between the hot and cold reservoirs, as well as the working substance used in the engine. The higher the temperature difference and the more efficient the working substance, the higher the efficiency of the engine.

5. Can a Carnot Heat Engine achieve 100% efficiency?

No, according to the second law of thermodynamics, it is impossible for any engine to achieve 100% efficiency. However, a Carnot Heat Engine can achieve the maximum theoretical efficiency for a given temperature difference between the hot and cold reservoirs.

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