Thermodynamics - Ideal gas expansion

[Chase11]

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.

 

[Andrew Mason]

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

 

[Chase11]

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]

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 V_i and V_f (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