Thermodynamics - Ideal gas expansion

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Homework Help Overview

The discussion revolves around a thermodynamics problem involving an ideal gas that undergoes isothermal expansion. The original poster is tasked with determining the number of moles of gas given specific heat input and volume change conditions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between heat (Q) and work (W) in isothermal processes, with some expressing uncertainty about how to proceed due to interdependencies between variables like the number of moles (n) and work done (W). There are attempts to express work in terms of known quantities, but confusion remains regarding the correct integration and application of the ideal gas law.

Discussion Status

Some participants have recognized the relationship Q = W for isothermal processes, which has led to further exploration of how to express the number of moles in terms of the given quantities. However, there is still a lack of consensus on the correct approach, with ongoing questions about the necessary variables and equations.

Contextual Notes

Participants note constraints such as the need for pressure to use the ideal gas equation and the challenge of deriving one variable from another without complete information. The discussion reflects the complexities of applying thermodynamic principles in this context.

Chase11
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Homework Statement


2.1E5 J of heat enters an ideal gas as it expands at a constant T = 77°C to four times its initial volume. How many moles of gas are there?

T=350K, Q=2.1E5 J, Vi=x, Vf=4x

Homework Equations


ΔU=Q-W
W=\intpdV
U=nCvT

The Attempt at a Solution



I'm not sure if I'm even on the right track here.
I have W=\intpdV = nRT\intdv/V = nRTln(Vf-Vi)
I am stuck here because I need to know n to solve for work but I need to know W to solve for n. I am clearly missing something but I can't figure out what it is.
 
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Chase11 said:

Homework Statement


2.1E5 J of heat enters an ideal gas as it expands at a constant T = 77°C to four times its initial volume. How many moles of gas are there?

T=350K, Q=2.1E5 J, Vi=x, Vf=4x


Homework Equations


ΔU=Q-W
W=\intpdV
U=nCvT

The Attempt at a Solution



I'm not sure if I'm even on the right track here.
I have W=\intpdV = nRT\intdv/V = nRTln(Vf-Vi)
I am stuck here because I need to know n to solve for work but I need to know W to solve for n. I am clearly missing something but I can't figure out what it is.
You are given Q. What is the relationship between Q and W if the process is isothermal?

AM
 
Yes thank you I realized yesterday that Q=W for an isothermal process. However I was still stuck after that. I feel like I should just use the ideal gas equation but I can't do that since I don't know pressure.
 
Chase11 said:
Yes thank you I realized yesterday that Q=W for an isothermal process. However I was still stuck after that. I feel like I should just use the ideal gas equation but I can't do that since I don't know pressure.
Express W in terms of n, T and Vi and Vf (check your equation for W - your integration is not correct). You have values for T, and Vf/Vi. If Q = W, express n in terms of Qm T, Vf/Vi

AM
 
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