Using the ideal gas law with two unknowns

[kaffekjele]

Homework Statement

You are given a closed container containing a single atom ideal gas.
The volume is V1= 0,45*10^(-3) m^3
Pressure p1 is 3,2 MPa
Temperature, T1, is 892 K

The volume of the gas is increased to V2= 8*V1

Find the pressure and temperature after the increase of volume.

Homework Equations

Ideal gas equation pV=nRT

The Attempt at a Solution

I have n= 0,19 moles from a previous question. R is the ideal gas constant, 8,31 J/moles*K

Manipulating the ideal gas equation for pressure gives me p = (nRT)/V but that leaves T as an unknown so I'm not sure if that's the right way to go...

 

[mfb]

I would expect that the expansion is adiabatic, this gives another constraint on the gas.

 

[kaffekjele]

I was looking at that and tried to find the new temperature by using T₂= T₁*($\frac{V1}{V2}$)^$\gamma-1$ which gave me 221,46K which is not correct according to my lecturer.

 

[mfb]

It would be interesting to see how the lecturer would solve this.

 

[Chestermiller]

I was looking at that and tried to find the new temperature by using T₂= T₁*($\frac{V1}{V2}$)^$\gamma-1$ which gave me 221,46K which is not correct according to my lecturer.

I get 223 K. What does your lecturer think about that answer?