Work done by a Carnot Engine. Melting ice

You should be able to solve for the 4th.In summary, the problem involves a Carnot engine with boiling water in the hot reservoir and ice water in the cold reservoir. 0.0400kg of ice melts in 5 minutes and the task is to determine the amount of work done by the engine. The relevant equations are Qh/Qc=Th/Tc, W=Qh-Qc, W=(1-Tc/Th)Qs, q=mHf, e=1-Tc/Th, e=W/Th, and the heat of fusion of water is 333.55kJ/kg. The first equation can be used to solve for the missing quantity, work done by the engine.
  • #1
The Real Simon

Homework Statement


The problem is that a Carnot contains Boiling water in the hot reservoir and ice water in the cold reservoir.
Given that 0.0400kg of ice is melted in 5 minutes, what is the amount of work done by the engine.

Homework Equations


Qh/Qc=Th/Tc
W=Qh-Qc
W=(1-Tc/Th)Qs
q=mHf
e=1-Tc/Th
e=W/Th
heat of fusion of water=Hf=333.55kJ/kg
I'm sure more are needed to solve it

3. The Attempt at a Solution
All I was able to solve is the energy transferred to the cold reservoir. q=0.0400kgx333.55kJ/kg=13.3kJ I think this is the Qc but really not sure.

Thanks for the help!
 
Physics news on Phys.org
  • #2
The Real Simon said:
All I was able to solve is the energy transferred to the cold reservoir. q=0.0400kgx333.55kJ/kg=13.3kJ I think this is the Qc but really not sure.
Yes, that's ##Q_c##. You now need to find the work done by the Carnot engine.
 
  • #3
Since you know Qc, you know 3 out of the 4 quantities in your first equation.
 

FAQ: Work done by a Carnot Engine. Melting ice

What is a Carnot Engine?

A Carnot Engine is an idealized heat engine that operates between two thermal reservoirs at different temperatures. It follows the Carnot cycle and is used as a model to understand the maximum efficiency that can be obtained from a heat engine.

How does a Carnot Engine work?

A Carnot Engine works by converting heat energy from a hot reservoir into mechanical work, and then rejecting any remaining heat to a cold reservoir. This process is repeated in a cyclical manner, with the engine returning to its initial state at the end of each cycle.

What is the efficiency of a Carnot Engine?

The efficiency of a Carnot Engine is given by the equation efficiency = (Thot - Tcold) / Thot, where Thot is the temperature of the hot reservoir and Tcold is the temperature of the cold reservoir. This means that the efficiency of a Carnot Engine is dependent on the temperature difference between the two reservoirs.

How does a Carnot Engine relate to melting ice?

A Carnot Engine is often used as a model to understand the process of melting ice. In this scenario, the hot reservoir represents the surroundings, while the cold reservoir represents the ice. The engine converts heat energy from the surroundings to melt the ice, with the efficiency depending on the temperature difference between the two.

How is the efficiency of a Carnot Engine affected by external factors?

The efficiency of a Carnot Engine is not affected by external factors, as it is an idealized model. In reality, factors such as friction and heat loss would decrease the efficiency. However, the Carnot efficiency remains the maximum efficiency that can be obtained from a heat engine operating between two temperatures.

Similar threads

Temperature in a Carnot heat engine
Replies
2
Views
2K
Heat Engine Efficiency: How Ice Water Affects Performance
Replies
1
Views
1K
Carnot engine efficiency problem
Replies
3
Views
4K
Work required to extract heat from a refrigerator
Replies
2
Views
1K
Efficiency of Stirling Cycle - Is it the same as the Carnot Engine?
Replies
14
Views
645
How do temperature differences affect the work done in an ideal Carnot process?
Replies
1
Views
1K
Efficiency and Temperature in Heat Engine Cycles: Approaching Parts B, C, and D
Replies
1
Views
912
Thermodynamics problem involving engine efficiency
Replies
20
Views
2K
Engine working between multiple temperature baths worse than Carnot
Replies
1
Views
1K
How much ice is melted in a Carnot engine using a hot and cold reservoir?
Replies
4
Views
3K

Hot Threads

Recent Insights

Back
Top