Thermodynamics - Ideal gas expansion

AI Thread Summary
The discussion revolves around calculating the number of moles of an ideal gas that absorbs 2.1E5 J of heat while expanding isothermally from an initial volume to four times that volume at a constant temperature of 77°C. Participants highlight the relationship between heat and work in an isothermal process, noting that Q equals W. The user struggles with the integration for work and the ideal gas equation due to the lack of pressure information. Suggestions are made to express work in terms of the number of moles, temperature, and volume ratios. The conversation emphasizes the need to correctly apply thermodynamic equations to solve for the unknowns.
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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