Corrected.Finding the Energy and Work in a Carnot Cycle

In summary: This may be the problem.In summary, the conversation involves calculating the energy expelled to the cold reservoir and the net work done by an ideal gas in a Carnot cycle. The gas takes in 1,200 J of energy from the hot reservoir during the isothermal expansion at 250°C and the isothermal compression at 50.0°C. The correct equation for finding the energy expelled to the cold reservoir is Qc = 0.381(1200J) = 457J, and the correct net work done by the gas is 741J when converting to Kelvin by adding 273.15. The conversation also includes a discussion on a typo in the calculation and converting to Kelvin.
  • #1
Feodalherren
605
6

Homework Statement


An ideal gas is taken through a Carnot cycle. The
isothermal expansion occurs at 250°C, and the isothermal
compression takes place at 50.0°C. The gas takes in 1 200 J
of energy from the hot reservoir during the isothermal
expansion. Find (a) the energy expelled to the cold reservoir
in each cycle and (b) the net work done by the gas in
each cycle.

Homework Equations


The Attempt at a Solution



Qh=1200J.

Qh-W=Qc (absolute values)

e(Carnot)=(523-323)/523= 61.9 %
(corrected my typo from before)

Therefore Qc= .381(1200J)=457J

and W = 1200-457=743J

Not the correct answer. Qc = 741 according to the solutions manual.

ps. Latex seems to be bugged, didn't work in "preview post" mode.
 
Last edited:
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  • #2
Feodalherren said:
e(Carnot)=1-(523/323)= 61.9 %

Hello. Check this calculation.
 
  • #3
Hi there.

Woops I typed it in wrong, it was supposed to be (523-323)/523= .619

The answer is still incorrect though.
 
  • #4
Feodalherren said:
Hi there.

Woops I typed it in wrong, it was supposed to be (523-323)/523= .619

The answer is still incorrect though.

That's not the problem. Check the numbers. Remember, you are looking for a difference of 2 joules.
 
  • #5
Give me another hint, please. I still don't know what I'm doing wrong :). Is my logic even sound?
 
  • #6
Feodalherren said:
Hi there.

Woops I typed it in wrong, it was supposed to be (523-323)/523= .619

The answer is still incorrect though.


e = (523-323)/523 is correct. But this does not equal .619
 
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  • #7
what?! How did I miss that, I re-did it like 3 times :/. Thank you though.
 
  • #8
Feodalherren said:
Hi there.

Woops I typed it in wrong, it was supposed to be (523-323)/523= .619

The answer is still incorrect though.


Also, to get the anwer of 741 J it appears that you should convert to Kelvin by adding 273.15 rather than 273.
 

Related to Corrected.Finding the Energy and Work in a Carnot Cycle

1. What is the Carnot cycle?

The Carnot cycle is a theoretical thermodynamic cycle that describes the most efficient way to convert heat into work. It consists of four reversible processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression.

2. How does the Carnot cycle work?

The Carnot cycle works by taking a gas through a series of four processes, each of which changes its temperature and pressure in a specific way. This results in the gas expanding and contracting, producing work that can be harnessed.

3. What is the maximum efficiency of the Carnot cycle?

The maximum efficiency of the Carnot cycle is given by the Carnot efficiency formula, which is equal to 1 - (Tc/Th), where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir. This means that the efficiency of the Carnot cycle is dependent on the temperatures of the two reservoirs and can never be greater than 1.

4. What is the significance of the Carnot cycle in thermodynamics?

The Carnot cycle is significant in thermodynamics because it provides a theoretical upper limit for the efficiency of any heat engine. This means that no real-world engine can ever be more efficient than the Carnot cycle. It also serves as a model for understanding the relationships between temperature, heat, and work in thermodynamic systems.

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

The Carnot cycle is used as a benchmark for evaluating the performance of real-world heat engines, such as steam turbines and gas engines. It is also the basis for the design of refrigeration and air conditioning systems, as well as heat pumps. Additionally, the principles of the Carnot cycle are applied in various industries, such as power generation and automotive engineering, to improve the efficiency of energy conversion processes.

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