How Do You Calculate Temperatures and Volumes in a Helium Gas PV Diagram Cycle?

[mrmonkah]

Homework Statement

100 moles of very dilute He gas are taken through the cycly ABC, where BC is an isothermal process. If P(a) = P(c) = 1atm, P(b) = 2atm and V(a) = V(b) = 3m^3, Calculate T(a), T(b) and V(c)

Homework Equations

eq1. PV = nRT
eq2. V = nRT/P

The Attempt at a Solution

Am i right in thinking that i can plug in the values of P(a) and V(a) to get T(a) into eq1. and similarly for T(b)?

I have T(a) = 361k, T(b) = 722k and V(c) = 6m^3

This seems to straight forward to be correct... any help would be great.

 

[Redbelly98]

The Attempt at a Solution

Am i right in thinking that i can plug in the values of P(a) and V(a) to get T(a) into eq1. and similarly for T(b)?

I have T(a) = 361k, T(b) = 722k and V(c) = 6m^3

This seems to straight forward to be correct... any help would be great.

Looks good, though I'm getting slightly different values for T(a) and T(b). You might want to recheck your calculation, and if you don't get slightly different results post your calculation of T(a) here. You are correct that T(b) is 2T(a), and V(c) is correct as well.

Did you use R=8.206 x 10^-5 atm·m³/(mol·K)?

 

[mrmonkah]

Hi Redbelly,

Ive submitted the work now. Unfortunately before seeing this post.

I actually converted my units to SI. And so used: R = 8.314J/(K mol)

Ive had some feed back in the past about sticking with the given units in some situations and not in others... and so i don't always head in the right direction. I am thinking in this example, stay with original units.

Cheers for the heads up.

Regards,
Dan

 

[Redbelly98]

No problem. Since you've submitted the work, I'll mention that I had gotten 366 K for T(a), so you were pretty close, only 1.3% off. I suspect you used the approximation 1 atm = 100 kPa, instead of the more accurate 1 atm = 101.3 kPa.