What Are the Temperatures of an Ideal Gas During an Adiabatic Expansion?

[coldjeanz]

Homework Statement

A 4.15 mol sample of a diatomic ideal gas (γ = 1.4) expands slowly and adiabatically from a pressure of 5.60 atm and a volume of 13.5 L to a final volume of 34.5 L.

Find initial+final temperatures

Homework Equations

pV/T (all initial) = pV/T (all final)

The Attempt at a Solution

First I was told to solve for the final pressure so I did that easily by doing:

P(final) = P(intial) * (Vi/Vf)^γ

and got 1.5 atm

I am confused on how you find the initial temp if they didn't give the final and vice versa. That's all I really need help with.

 

[ehild]

I am confused on how you find the initial temp if they didn't give the final and vice versa. That's all I really need help with.

Use the Ideal Gas Law PV=nRT

ehild

 

[coldjeanz]

But how does that differentiate between the initial and final temp?

P (final-initial) * V (final-initial) = n*R*T(final-initial)

I still have two unknowns then.

 

[ehild]

Two unknowns, two equations.
Read the problem carefully. What is the initial pressure and temperature? What is n, the number of moles? Can you calculate the initial temperature from PV=nRT?

ehild

 

[coldjeanz]

Ok so you set one up using all the initial values and then another using all the final values?

I tried doing this for the initial temp but it's still saying I'm getting the wrong answer...

pV=nRT

(5.6 atm)*(13.5 L) = (4.15 mol)*(8.314 J/mol*K)(T)

I get something like 2.2 and since it wants the answer in K I added 273.15 and I rounded to 276 but it's not right.

 

[ehild]

Without units, the numbers do not mean anything. In what unit is that 2.2? What units do you have to use for the pressure, temperature and volume in the equation

PV=8.314 J/(mol K) n T?

ehild