# Thermodynamics - Ideal gas expansion

## 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=$\int$pdV
U=nCvT

## The Attempt at a Solution

I'm not sure if I'm even on the right track here.
I have W=$\int$pdV = nRT$\int$dv/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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Andrew Mason
Homework Helper

## 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=$\int$pdV
U=nCvT

## The Attempt at a Solution

I'm not sure if I'm even on the right track here.
I have W=$\int$pdV = nRT$\int$dv/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.

Andrew Mason