How much ice is melted in a Carnot engine using a hot and cold reservoir?

In summary, in this conversation, a Carnot engine using a hot reservoir of boiling water and a cold reservoir of ice and water is discussed. The question asks how many kilograms of ice in the tub are melted when 6437 J of heat is put into the engine and work is produced. The equations used are Q=m*(deltaHf) and efficiency=1-(T_cold/T_hot). After some online research, the efficiency is found to be 0.268 and the heat of fusion for water is 3.34E5 J/kg. Using these values, the work output and remaining heat going into the cold reservoir are calculated. It is then determined that 73.2% of the added energy should be delivered as
  • #1
rlc
128
1

Homework Statement


A Carnot engine uses a hot reservoir consisting of a large amount of boiling water and a cold reservoir consisting of a large tub of ice and water. When 6437 J of heat is put into the engine and the engine produces work, how many kilograms of ice in the tub are melted due to the heat delivered to the cold reservoir?

Homework Equations


Q=m*(deltaHf)
efficiency=1-(T_cold/T_hot)

The Attempt at a Solution


Searching online, I found those equations but nothing is working for me.
With the efficiency, I found:
1-(273/373)=0.268
And the heat of fusion for water is 3.34E5 J/kg

What am I missing?
 
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  • #2
rlc said:
With the efficiency, I found:
1-(273/373)=0.268
And the heat of fusion for water is 3.34E5 J/kg
Given the efficiency and the quantity of heat input, how much work is output? How much heat is left to go into the cold reservoir?
 
  • #3
You know T1 and T2 and Q1. Using zero universe entropy change as your criterion you can figure out Q2 and then of course the amount of ice meltred. Assume there is still ice left at T2 when the process ends (T2 is constant = 273K).
 
  • #4
Would the work output be the efficiency times the J heat put into the engine?
 
  • #5
Aha! I figured it out!
100-26.8% = 73.2%--of the added energy should be delivered as heat to the cold reservoir.
deltaH=m(Lf)
(0.732)(6437J)=m(3.34E5J/kg)
m=0.0141 kg ice melted

Thank you both for helping me!
 

FAQ: How much ice is melted in a Carnot engine using a hot and cold reservoir?

1. What is a Carnot Engine?

A Carnot Engine is a theoretical engine that operates on the Carnot cycle, which is a thermodynamic cycle that is the most efficient possible for a heat engine. It was first proposed by French physicist Sadi Carnot in 1824.

2. How does a Carnot Engine work?

A Carnot Engine works by converting heat energy into mechanical work. It does this by using a heat source, such as a hot reservoir, to heat up a working fluid, which then expands and pushes a piston. The piston is connected to a crankshaft, which converts the linear motion into rotational motion.

3. What is the efficiency of a Carnot Engine?

The efficiency of a Carnot Engine is determined by the ratio of the temperature difference between the hot and cold reservoirs. It is given by the formula: Efficiency = 1 - (Tcold/Thot), where Tcold is the temperature of the cold reservoir and Thot is the temperature of the hot reservoir.

4. How is heat delivered in a Carnot Engine?

In a Carnot Engine, heat is delivered by the expansion of the working fluid, which causes it to do work. The heat is then converted into mechanical energy, which can be used to power a machine or device.

5. What are the practical applications of a Carnot Engine?

Although a Carnot Engine is a theoretical concept, the principles of the Carnot cycle are used in real-life applications, such as refrigerators and heat pumps. These devices use the Carnot cycle to transfer heat from a cold reservoir to a hot reservoir, allowing for the cooling or heating of a space or object.

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