Calculating q, w, H, and U for an Ideal Gas at 25°C and 100kPa

  • Thread starter Thread starter chocolatepie
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around calculating work (w), heat (q), change in internal energy (U), and change in enthalpy (H) for an ideal gas undergoing a reversible isothermal expansion from 100 kPa to 5 kPa at 25°C. Participants explore various equations and concepts related to thermodynamics, particularly in the context of ideal gases.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses uncertainty about how to approach the problem and seeks direction.
  • Another participant suggests that a reversible isothermal process is a polytropic process and questions the value of n in this context.
  • There is a discussion about the role of molar volume and its relation to the ideal gas law.
  • Some participants clarify that in an isothermal process, the change in internal energy (ΔU) is zero.
  • One participant proposes using the formula for work done in a reversible process, Wrev = nRT ln(P2/P1), but notes the absence of the number of moles (n) in the problem statement.
  • Clarifications are made that calculations should be done per mole, implying n=1 mol.
  • Participants debate which formula to use for calculating change in enthalpy (ΔH), with some suggesting ΔH = qp and others pointing out the conditions under which these formulas apply.
  • There is confusion regarding the conditions of the expansion, particularly the distinction between constant pressure and constant temperature.
  • One participant mentions a formula involving heat capacity but notes the lack of provided values for heat capacity in the question.
  • Another participant highlights that ΔH = ΔU + ΔngasRT is applicable for ideal gases.

Areas of Agreement / Disagreement

Participants express various viewpoints and uncertainties regarding the appropriate equations and conditions for the problem. There is no consensus on the best approach to calculate the required values, and multiple competing views remain on how to interpret the problem's conditions.

Contextual Notes

Participants note that the expansion does not occur at constant pressure, which affects the applicability of certain formulas. There is also mention of missing assumptions and the need for specific values (like heat capacity) that are not provided in the question.

chocolatepie
Messages
28
Reaction score
0

Homework Statement


An ideal gas at 25degree celsius and 100kPa is allowed to expand reversibly and isothermally to 5kPa. Calculate..
1) w per mol (J/mol)
2) q per mol (J/mol)
3) change in molar internal energy U (J/mol)
4) change in molar enthalpy H (J/mol)


Homework Equations



ΔU = q + w
= q - pextΔV
ΔH = ΔU +p ΔV
= ΔU + ΔngasRT
PV=nRT
Um(T)=3/2RT

The Attempt at a Solution



I absolutely have no idea how to do this question. Any direction would be greatly appreciated.
 
Physics news on Phys.org
Welcome to the forum.
Hint:
A reversible isothermal process is a polytropic process where PV^n = constant. What is n for this kind of process?
 
I am thinking this question should include a molar volume? (molar volume = V/n, which changes the ideal gas law as P(molar volume) = RT?)

n is constant for this kind of process? but that sounds weird.. sorry I am lost..

Also, since it is an isothermal process, would molar U be 0?
 
Welcome to PF, chocolatepie! :smile:

An isothermal process is one in which T is constant.
So molar U will not be zero, but constant.
In other words: ΔU=0.

With constant T=To, you get for one mole: PV=RTo.

To calculate w you need to integrate dw=-PdV.
Do you know how to do that?
 
I assuming we need to use Wrev= nRT ln (P2/P1) to solve.
However, we were not given n value...?

PS. And thanks everyone for the warm welcome to PF :D
 
chocolatepie said:
I assuming we need to use Wrev= nRT ln (P2/P1) to solve.

Yep. That will work.


chocolatepie said:
However, we were not given n value...?

n is the number of moles.
The question asks to calculate "per mol".
This means you should calculate using n=1 mol.


chocolatepie said:
PS. And thanks everyone for the warm welcome to PF :D

You're welcome! :wink:
 
n is the number of moles.
The question asks to calculate "per mol".
This means you should calculate using n=1 mol.

oh, OK!
And for part (d) where I need to calculate for the change of molar enthalpy, should I use ΔH = qp to solve? or ΔH = ΔU + pΔV?

I just don't know when to use each formula..
 
chocolatepie said:
oh, OK!
And for part (d) where I need to calculate for the change of molar enthalpy, should I use ΔH = qp to solve? or ΔH = ΔU + pΔV?

I just don't know when to use each formula.

Actually, neither formula.
Both have conditions attached.

ΔH = qp only holds in an isobaric process.
ΔH = ΔU + pΔV also only holds in an isobaric process (is this really the formula you have?)

What else do you have for ΔH?
 
The note at the bottom of the question says that the expansion does not occur at constant pressure. Thus, iti s not OK to use ΔH = ΔU + pΔV.
I am not sure why the note says "constant pressure" when the question itself says "constant temperature" :-O

I have one that includes heat capacity..? H=CpT (subscript p = const P)
But I don't have the heat capacity given in the question, so I didn't use it.
 
  • #10
chocolatepie said:
The note at the bottom of the question says that the expansion does not occur at constant pressure. Thus, iti s not OK to use ΔH = ΔU + pΔV.
I am not sure why the note says "constant pressure" when the question itself says "constant temperature" :-O

I have one that includes heat capacity..? H=CpT (subscript p = const P)
But I don't have the heat capacity given in the question, so I didn't use it.

In your relevant equations you have:
ΔH = ΔU + ΔngasRT
(Works only for ideal gasses.)

What about that one?Btw, Cp=Cv+R for ideal gasses.
And ΔH = ΔU + Δ(PV) is true in general.
 
  • #11
Aha, now I got it. Yes there was a formula on my note.
Thank you so much!
 
  • #12
See you! :smile:
 

Similar threads

Replies
9
Views
3K
  • · Replies 10 ·
Replies
10
Views
4K
  • · Replies 11 ·
Replies
11
Views
6K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 16 ·
Replies
16
Views
3K
Replies
2
Views
6K