Volume, pressure and final temperature

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Discussion Overview

The discussion revolves around a homework problem involving the properties of air under specific conditions, including initial temperature, pressure, and volume, as well as the application of the ideal gas law and a specific relation between pressure and volume. The scope includes mathematical reasoning and technical explanation related to thermodynamics.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant seeks guidance on solving for the initial volume, final pressure, and final temperature of air given specific conditions.
  • Another participant emphasizes the importance of showing work before receiving answers, indicating a collaborative approach to problem-solving.
  • A participant converts the initial temperature from Celsius to Kelvin, stating the conversion as 773.15 K.
  • Concerns are raised about the application of the ideal gas law and the relation pV1.2 = c, with one participant pointing out a potential error in mixing initial pressure and final volume.
  • Participants discuss the molar mass of air, with one stating it as 29 g/mol and another calculating the number of moles based on the mass of air provided.
  • There is a calculation presented for the number of moles, with one participant arriving at 4.1379 moles and seeking confirmation of its correctness.

Areas of Agreement / Disagreement

Participants generally agree on the need to show work and the importance of correct calculations. However, there is disagreement regarding the correct application of the ideal gas law and the calculations for the number of moles, with some participants questioning earlier calculations.

Contextual Notes

There are unresolved issues regarding the application of the ideal gas law in conjunction with the given relation pV1.2 = c, as well as the accuracy of the calculations for the number of moles of air.

Ben_Walker1978
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Homework Statement



a) A mass of 0.12 kg of air has an initial temperature of 500°C and pressure 0.8 MPa. If the air is expanded according to the law pV1.2 = c to a final volume of 90 litres, determine
i) its initial volume,

ii) its final pressure,

iii) its final temperature.
For air, take R = 287 Jkg¯¹ K¯¹.

Homework Equations


pV1.2 = c
pV = nRT
n = pxV / RxT

The Attempt at a Solution



Can anyone point me in the right direction?
As i have no clue how to complete this.
Thanks.
 
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We aren't allowed to give the answer unless you show us your work attempting a solution. "No clue" is not enough.
 
Hello.

i have done a bit of working out.

I converted celsius to kelvin. Which is 773.15

i think 1.2 is how dry the air is?

n = 0.8 x 90 / 287 x 773.15 = 193.96

So n = 193.96

So i have all the information for the equations.

Is is just pV1.2 = c
 
Ben_Walker1978 said:
n = 0.8 x 90 / 287 x 773.15 = 193.96
This will not work. You have mixed the initial pressure and final volume.

Part one asks for the initial volume. How could you use the ideal gas law and the given relation ##1.2pV=c## to find this?
 
Last edited:
How many gram moles of air does 0.12 kg represent?
 
Last edited:
i thought i worked this out in my previous post.

The molar mass of air is 29g/mol
 
Ben_Walker1978 said:
The molar mass of air is 29g/mol
So what is ##n## in this case?
 
Ben_Walker1978 said:
i thought i worked this out in my previous post.

The molar mass of air is 29g/mol
I don't see it there. If the molar mass of air is 29 g/mol, how many gram moles of air does 0.12 kg represent? It is definitely not 194.
 
3.48?
 
  • #10
Ben_Walker1978 said:
3.48?
Please show how you arrived at this number?
 
  • #11
I have worked it out i think.

0.12kg / 0.029kg/mol = 4.1379

Is this correct?
 
  • #12
Ben_Walker1978 said:
I have worked it out i think.

0.12kg / 0.029kg/mol = 4.1379

Is this correct?
Yes. Now you know the number of moles, the initial temperature, and the initial pressure. So, from the ideal gas law, what is the initial volume ##V_i##?
 

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