Thermodynamics - Adiabiatc Expansion

[kineticwave]

Homework Statement

2.5 mol of an ideal gas which starts at 2.2 atm and 50 degrees Celsius does 2.4 kJ of work during an adiabatic expansion. What is the final volume of the gas? Express the result in the unit [m3].

Homework Equations

V(initial) x T(initial)^(3/2) = V(final) x T(final)^(3/2)

The Attempt at a Solution

I found the initial volume first using pV=nRT which I got to be 30.15L. But I'm not sure how to get the final temperature, nor the final volume for that matter.

 

[haruspex]

What's the internal energy of the gas? How does a change in that relate to work done?

 

[kineticwave]

What I've posted is literally all the information I was given when asked to complete the question... my professor is known for his incomprehensible and ambiguous questions.

 

[Andrew Mason]

What I've posted is literally all the information I was given when asked to complete the question... my professor is known for his incomprehensible and ambiguous questions.

It is not possible to answer this question without knowing the heat capacity of the gas. You appear to be using 1/(γ-1)=3/2 which would make Cv = 3/2 and γ = 5/3

Are you told that this is a monatomic gas?

AM

 

[kineticwave]

The question posted is all that I'm given. This professor is known for questions like these. It's a course called Biophysics.

 

[Andrew Mason]

The question posted is all that I'm given. This professor is known for questions like these. It's a course called Biophysics.

So how do you know that 1/(γ-1) = 3/2? (you have put this in your equation). Only a monatomic gas would have Cv=3R/2; γ=5/3.

AM

 

[henry407]

Just a thought
ΔU=nR∫(T/V)dV
where T can be represent by V
(V_ixT_i)^3/2)=(VxT)^3/2=constant <-- calculate by sub initial conditions.

 

[Andrew Mason]

Just a thought
ΔU=nR∫(T/V)dV

Ok except for a - sign. If Q = 0 then ΔU = -∫PdV

where T can be represent by V

??How do you do that?

AM

 

[henry407]

Re AM:
(VixTi)^3/2=(VxT)^3/2=constant
isn't it, since the whole process is Adiabiatic Expansion, the above equation satisfy in any time during the process.

 

[Andrew Mason]

Re AM:
(VixTi)^3/2=(VxT)^3/2=constant
isn't it, since the whole process is Adiabiatic Expansion, the above equation satisfy in any time during the process.

Ok. I see what you mean. That will work.

AM