Thermodynamics Energy transfer question

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Discussion Overview

The discussion revolves around a thermodynamics problem involving a frictionless piston-cylinder system containing R-134a. Participants explore the effects of heat transfer on the refrigerant's final temperature, considering different assumptions about the process, such as constant pressure and constant volume. The conversation includes attempts to solve the problem and clarify the correct application of thermodynamic equations.

Discussion Character

  • Homework-related
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant assumes constant pressure for the process and uses the equation Q - Wb = ΔH, but struggles to find the boundary work due to lack of information on v2.
  • Another participant argues that for constant pressure expansion, the equation Q = ΔH should be used, suggesting that knowing Q allows for determining the final enthalpy and subsequently the final temperature from tables.
  • Some participants express confusion over the role of boundary work in the process, questioning why it might not be considered in a piston-cylinder system.
  • There are conflicting results regarding the final temperature, with one participant calculating 59.4 °C and another suggesting a different approach yields around 63 °C.
  • One participant mentions that the system indicates a correct answer of 34.3 °C, prompting questions about how this value could be obtained.
  • Participants express uncertainty about the correctness of their calculations and the problem statement, with one confirming they provided the entire problem as stated.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct approach to the problem or the final temperature. Multiple competing views remain regarding the application of thermodynamic principles and the role of boundary work.

Contextual Notes

There are limitations in the discussion regarding assumptions made about the process (constant pressure vs. constant volume) and the potential for errors in calculations. The exact conditions and parameters of the problem may not be fully clarified.

Silverhobbiest
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Homework Statement


In a frictionless piston-cylinder system, there are 3 kg of R-134a initially at 280 kPa and 15 °C. Heat is transferred to the system in the amount 120 kJ. What will the final temperature of the refrigerant be (deg C)?

Homework Equations


Q - W = ΔU (internal energy)
Q - Wb (boundary work) = ΔH (enthalpy)
(if pressure is constant) Wb = P(v2-v1)

[where v is specific volume]

The Attempt at a Solution


I assumed that pressure was constant for this problem because the piston is implied to be free to move. Also, I know that there is boundary work because if the piston is free to move then the volume is changing.

So, I used the equation:
Q - Wb = ΔH

I identified the refrigerant to be in the superheated vapor phase and used the property tables to calculate the specific volume to the refrigerant at the initial state and got 0.078215 m3/kg and calculated the enthalpy to be 264.12kJ/kg.

I was then stuck on how to find boundary work because I have no idea how to find v2 with the given information. I planned on calculating boundary work so that I can use the equation to solve for h2 and then use the property tables to locate the temperature of the substance.

I became frustrated and attempted to ignore it entirely and got an incorrect answer of 59.4 degrees celsius.

How do I find boundary work? Is my approach correct? Please help me solve thi problem so that I can understand what I'm doing wrong.
 
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If the expansion takes place at constant pressure, the equation you used is incorrect. The correct equation to use for constant pressure expansion is $$Q=\Delta H$$Since you know Q, you also know ##\Delta H##. That means that you know the final enthalpy per unit mass. You then use your tables to find the final temperature that gives that value for the final enthalpy.
 
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Chestermiller said:
If the expansion takes place at constant pressure, the equation you used is incorrect. The correct equation to use for constant pressure expansion is $$Q=\Delta H$$Since you know Q, you also know ##\Delta H##. That means that you know the final enthalpy per unit mass. You then use your tables to find the final temperature that gives that value for the final enthalpy.

I initially did it this way and got 59.4 °C, but that was incorrect. That is what led me to believe that there was boundary work involved because the process takes place inside of a piston cylinder system. So, why isn't boundary work supposed to be considered in this process?
 
Silverhobbiest said:
I initially did it this way and got 59.4 °C, but that was incorrect. That is what led me to believe that there was boundary work involved because the process takes place inside of a piston cylinder system. So, why isn't boundary work supposed to be considered in this process?
Maybe they expected you to assume constant volume, and maybe you made a mistake in the calculation. If you want, I'll redo the constant pressure calculation.
 
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I pretty much confirm your final temperature for the heating at constant pressure.
 
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Chestermiller said:
I pretty much confirm your final temperature for the heating at constant pressure.
Okay, then I'll just email the instructor to see if it's another error in the system. Thank you very much for helping me!
 
Silverhobbiest said:
Okay, then I'll just email the instructor to see if it's another error in the system. Thank you very much for helping me!
For constant volume, I get something around 63 C.
 
Chestermiller said:
For constant volume, I get something around 63 C.

According to the system, the correct answer is 34.3 C. Do you know anyway this answer could have been obtained?
 
Silverhobbiest said:
According to the system, the correct answer is 34.3 C. Do you know anyway this answer could have been obtained?
No. Have you given the entire problem statement, word for word?
 
  • #10
Chestermiller said:
No. Have you given the entire problem statement, word for word?
Yes I have.
 
  • #11
Silverhobbiest said:
Yes I have.
Well, then I don't see how they get that answer.
 

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