Thermodynamic Application Isothermal Work

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Homework Help Overview

The discussion revolves around a thermodynamic problem involving an ideal gas that performs isothermal work during expansion. Participants are tasked with determining the initial volume and temperature of the gas given specific work done and final conditions.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between work, volume, and temperature in the context of isothermal processes, referencing the equation W = nRTln(vi/vf). There is uncertainty about how to isolate variables, particularly temperature and initial volume, given the constraints of the problem.

Discussion Status

Several participants express frustration with the complexity of the problem and question the logical consistency of their calculations. Some suggest starting with the ideal gas law to find temperature, while others explore the implications of the work done on the initial volume. There is no explicit consensus, but multiple lines of reasoning are being explored.

Contextual Notes

Participants note the importance of unit consistency, particularly when converting volume from liters to cubic meters. There is also mention of the potential for illogical results if assumptions or calculations are incorrect.

latitude
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Homework Statement



One mole of an ideal gas does 3000 J work on its surroundings as it expands isothermally to a final pressure of 1 atm and volume 25 L. Determine a) initial volume and b) Temp of gas

Homework Equations

The Attempt at a Solution


Well, its isothermal, so Temp is constant, so
W = nRTln(vi/vf)
It says it expands, so the initial volume is <25 L...
that's kinda all I got right now; I'm not sure how to get the next step, since both T and vi are in the equation. It must have something to do with pressure.
 
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latitude said:

Homework Statement



One mole of an ideal gas does 3000 J work on its surroundings as it expands isothermally to a final pressure of 1 atm and volume 25 L. Determine a) initial volume and b) Temp of gas

Homework Equations

The Attempt at a Solution


Well, its isothermal, so Temp is constant, so
W = nRTln(vi/vf)
It says it expands, so the initial volume is <25 L...
that's kinda all I got right now; I'm not sure how to get the next step, since both T and vi are in the equation. It must have something to do with pressure.
How do you find the temperature of the gas? Find that and then determine what ln(vi/vf) has to be if W=3000J.

AM
 
PV = nRT
(1.013 x 10^5)(10 m^3) = (1)(8.314)T
T = Some really big, way illogical number? Unless the moles thing is wrong...

ARGH. This one is frustrating me. I'm wondering if I don't have to find volume first??
 
Last edited:
Oooh...

3000 J = nR(PV/nR)(ln(vi/vf))
3000 J = (10.13 x 10^5)(25 L) ln(vi/25)
1.184 x 10^-3 = vi/25
vi = 0.029 L??

Possible??

EDIT: No, cause my final temp is still 304606.7 K !
 
Last edited:
latitude said:
Oooh...

3000 J = nR(PV/nR)(ln(vi/vf))
3000 J = (10.13 x 10^5)(25 L) ln(vi/25)
1.184 x 10^-3 = vi/25
vi = 0.029 L??

Possible??

EDIT: No, cause my final temp is still 304606.7 K !
Start with PV=nRT

[tex]P_iV_i = nRT = P_fV_f[/tex]

You know [itex]P_f, V_f[/itex] and n so work out T. Be careful to use the correct units for volume. Units are litres or 10^-3 m^3.


Then, from W = nRTln(vi/vf), work out what vi is.

AM
 

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