Thermodynamics- carnot engine power

In summary, we have a reversed Carnot engine in an ice making plant that is extracting heat from a well-insulated box. The temperature in the icebox is -5C and the temperature of the ambient air is 30C. With an initial water temperature of 30C, 10,000kg of ice is produced. The homework equations used include Qwater, Qfreeze, and Qice, and the goal is to determine the required mechanical power. The c.o.p. and the time frame for making the ice are not specified in the problem statement. There may also be a discrepancy between mechanical power and mechanical energy.
  • #1
emg333
3
0

Homework Statement



An ice making plant consists of a reversed Carnot engine extracting heat from a well- insulated box. The temperature in the icebox is -5C and the temperature of ambient air is 30C. Water of an initial temp 30C is placed in the icebox and allowed to freeze and cool to -5C. If the plant makes 10,000kg of ice, what is the mechanical power required?

Homework Equations



Qwater= c(water)*m*(T2-T1)
Qfreeze= Latent heat of fusion * m
Qice= c(ice)*m*(T2-T1)

n= 1- Q2/Q1

The Attempt at a Solution



I calculated Qwater, Qfreeze, and Qice. I am not sure where to go from here
 
Physics news on Phys.org
  • #2
Okay, so that gives you the amount of heat that is removed from the water. We need to relate that to the work done.

What is the c.o.p. (coefficient of performance) for a refrigerator?

p.s. I see a problem with the way the problem statement is worded. Does it say in how much time the 10,000 kg ice must be made? And, does it ask for mechanical power or mechanical energy?
 
  • #3
.



To find the mechanical power required for the ice making plant, we can use the equation for efficiency of a Carnot engine (n=1-Q2/Q1). In this case, Q1 represents the heat extracted from the icebox (Qwater+Qfreeze) and Q2 represents the heat rejected to the ambient air (Qice). We can plug in the values we calculated for Qwater, Qfreeze, and Qice to find the efficiency of the engine. Then, we can use the equation for power (P=Q/t) to determine the mechanical power required for the plant. It is important to note that this calculation assumes ideal conditions and does not take into account any losses or inefficiencies in the system.
 

1. What is a Carnot engine?

A Carnot engine is a theoretical engine that operates on the principles of thermodynamics and is used to model the maximum possible efficiency of a heat engine. It consists of two isothermal processes and two adiabatic processes, and is often used in comparison to real engines to determine their efficiency.

2. How does a Carnot engine work?

A Carnot engine works by using a heat source to convert thermal energy into mechanical work. This is achieved through a series of processes, including isothermal expansion and compression, and adiabatic expansion and compression. The engine operates in a cycle, with the goal of maximizing the amount of work output for a given amount of heat input.

3. What is the efficiency of a Carnot engine?

The efficiency of a Carnot engine is given by the ratio of the work output to the heat input. This is known as the Carnot efficiency and is represented by the equation: efficiency = (Th - Tc) / Th, where Th is the temperature of the hot reservoir and Tc 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.

4. How is the power output of a Carnot engine determined?

The power output of a Carnot engine is determined by the amount of work it can produce in a given time. This is affected by the efficiency of the engine, as well as the amount of heat being input into the system. The power output can be calculated using the equation: power = efficiency x heat input.

5. What are some real-world applications of Carnot engines?

While Carnot engines are primarily used as theoretical models, they have real-world applications in certain industries. For example, some power plants use a variation of the Carnot cycle to generate electricity. They are also used in some refrigeration systems and heat pumps. However, due to practical limitations, the efficiency of these real-world applications is often lower than the theoretical maximum efficiency of a Carnot engine.

Similar threads

  • Introductory Physics Homework Help
Replies
1
Views
928
  • Introductory Physics Homework Help
Replies
3
Views
874
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
907
  • Introductory Physics Homework Help
Replies
17
Views
2K
Replies
2
Views
674
  • Introductory Physics Homework Help
Replies
8
Views
663
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
2K
Back
Top