Calculating Final Pressure of an Adiabatic Gas Expansion

[fiziks09]

Homework Statement

As a 1.00 mol sample of a monoatomic gas expands adiabatically the work done on it is
-2.50x10^3J. The initial temperature and pressure of the gas are 500k and 3.60atm. Calculate
a. The final temperature and b. The final pressure.

Homework Equations

First law of thermodynamics
Eint = Q + W

The Attempt at a Solution

I was able to solve the first part of the question. Since it was an adiabatic process Q = 0 and then used Eint = nCv(Tb - Ta) to get the final temperature which is 300k.

But i can't seem to get the final pressure. I have no idea on how to begin. Please any help will be very much appreciated.

 

[Thaakisfox]

Use the state equation for an adiabatic process i.e. p*T^(k/(1-k))=constant. Where k is the quotient of the heat capacities.

 

[fiziks09]

quotient of heat capacities?? please i don't understand that part!

 

[Thaakisfox]

Its just that k=C_p/C_v. The quotient of the heat capacities at constant pressure and constant volume.

 

[fiziks09]

okay..i get that part.. is the constant R??

 

[Thaakisfox]

No... that equation means that this quantity p*T^(k/(1-k)) is constant throughout the process. Which means that its the same in the beginning and at the end. U know the pressure and temperature at the beginning you know tht temp at the end...

 

[fiziks09]

ok.. but I'm getting a wrong answer which is 5.9atm but it should be 1atm...

 

[Thaakisfox]

Are you making your calculations correctly? what's the value you got for k for the gas?

 

[fiziks09]

i got 1.5
i used C_v to be 3/2R since the gas is monoatomic and C_p to be 5/2R

 

[Thaakisfox]

shouldnt it be 1.667? And then what's the next step? show the whole calculation otherwise i can't see wtz wrong...