Thermodynamics - closed systems

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Discussion Overview

The discussion revolves around a thermodynamics problem involving a closed system with a piston containing air. Participants are tasked with determining the index n in a compression process governed by the law PVn = const., as well as calculating changes in internal energy and final pressure after a series of thermodynamic processes. The scope includes theoretical analysis and mathematical reasoning related to thermodynamic principles.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses uncertainty about finding the value of n without knowing T2, suggesting a need for further information.
  • Another participant questions whether T2 could be equal to T1, indicating a potential simplification in the analysis.
  • A participant points out an error in the relevant equation's formatting, noting that the exponent is incorrectly written and could lead to misunderstanding.
  • Another participant suggests that the ratios of specific volumes and pressures provide sufficient information to determine the value of n.

Areas of Agreement / Disagreement

Participants do not reach a consensus on how to proceed with finding n, as there are differing opinions on the relationship between T1 and T2, as well as the interpretation of the relevant equations.

Contextual Notes

There are unresolved issues regarding the assumptions made about temperature relationships and the correct formatting of equations, which may affect the clarity of the problem-solving approach.

Who May Find This Useful

This discussion may be useful for students and practitioners interested in thermodynamics, particularly those dealing with closed systems and compression processes in gases.

MegaDeth
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Homework Statement


A cylinder fitted with a piston contains air at 1.0 Bar and 17°C. The gas is compressed according to the law PVn = const., until the pressure is 4 bar when the specific volume is found to be 28% of the initial value. Heat is then added to the air at constant pressure until the volume is doubled. The same amount of heat is now removed from the air at constant volume.

Determine the value of the index n in the compression process.
Find also
(a) the overall change in internal energy/kg of air and
(b) the final pressure of the air.


R = 0.287 kJ/kgK, Cp = 1.005718kJ/kgK

Homework Equations


(ps/p1) = (T2/T1)(n/n - 1)



The Attempt at a Solution


4 = (T2/290)(n/n - 1)

I'm not sure how to find n seeing as I haven't got T2, any ideas?
 
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MegaDeth said:

Homework Statement


A cylinder fitted with a piston contains air at 1.0 Bar and 17°C. The gas is compressed according to the law PVn = const., until the pressure is 4 bar when the specific volume is found to be 28% of the initial value. Heat is then added to the air at constant pressure until the volume is doubled. The same amount of heat is now removed from the air at constant volume.

Determine the value of the index n in the compression process.
Find also
(a) the overall change in internal energy/kg of air and
(b) the final pressure of the air.


R = 0.287 kJ/kgK, Cp = 1.005718kJ/kgK

Homework Equations


(ps/p1) = (T2/T1)(n/n - 1)

The Attempt at a Solution


4 = (T2/290)(n/n - 1)

I'm not sure how to find n seeing as I haven't got T2, any ideas?

Isn't T2 = T1?
The same amount of heat is now removed from the air at constant volume.

BTW, your relevant equation is incorrectly written. In some places you have more parentheses than you need (e.g., (ps/p1) is the same as ps/p1 ) , and in the exponent on the right side, there are not enough of them.

Your exponent, as written, is equal to zero. n/n - 1 is the same as (n/n) - 1 = 1 - 1 = 0. If you mean ##\frac{n}{n - 1}## rather than ##\frac n n - 1##, write it as (n/(n - 1)).
 
How will that work then?
 
You know the ratio of the specific volumes and the ratio of the pressures. This gives you enough information to get n.
 

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