Thermo: Need help finding T2 and V2 in an adiabat

[Courtknee]

Homework Statement

1 mole of ideal gas initially at 294 K is compressed adiabatically and
reversibly from 0.83 atm to 10.0 atm. Calculate the initial and …final volumes,
the final temperature, $\Delta$U; $\Delta$H; Q; and W: Assume that Cv = (5/2)R

Given:

n = 1 mol
T1 = 294 K
P1 = 0.83 atm
P2 = 10 atm
Q = 0

Find
V1, V2, $\Delta$U, Q, $\Delta$H, T2, W

Homework Equations

1. The professor gave that specific heat at constant volume is (5/2)R, however, the volume of the problem changes. Is this equation completely irrelevant to the problem?

2. How to you find the final temperature and final volume?

The Attempt at a Solution

I started off with PV = nRT for the initial givens and obtained that V1 = 29.1 L

Now, I'm stuck. I've tried using the ideal gas equation again, but I have 2 unknowns. I tried rearranging the equation and setting it equal the initial equations. I know how to find the other unknowns, but I'm stuck at this part for some reason.

 

[Andrew Mason]

Homework Statement

1 mole of ideal gas initially at 294 K is compressed adiabatically and
reversibly from 0.83 atm to 10.0 atm. Calculate the initial and …final volumes,
the final temperature, $\Delta$U; $\Delta$H; Q; and W: Assume that Cv = (5/2)R

Given:

n = 1 mol
T1 = 294 K
P1 = 0.83 atm
P2 = 10 atm
Q = 0

Find
V1, V2, $\Delta$U, Q, $\Delta$H, T2, W

Homework Equations

1. The professor gave that specific heat at constant volume is (5/2)R, however, the volume of the problem changes. Is this equation completely irrelevant to the problem?

2. How to you find the final temperature and final volume?

The Attempt at a Solution

I started off with PV = nRT for the initial givens and obtained that V1 = 29.1 L

Now, I'm stuck. I've tried using the ideal gas equation again, but I have 2 unknowns. I tried rearranging the equation and setting it equal the initial equations. I know how to find the other unknowns, but I'm stuck at this part for some reason.

You need to use the adiabatic condition: $PV^\gamma = constant = K$ which can be rewritten: $TV^{\gamma-1} = K/nR = constant$

AM

 

[Courtknee]

I'm assuming that the constant K will remain the same for p1*v1 and p2*v2

If I set P₁V₁^γ = K, then I can use that constant for P₂V₂^γ and obtain the volume, correct?

 

[Andrew Mason]

I'm assuming that the constant K will remain the same for p1*v1 and p2*v2

If it didn't, it would not be constant!

If I set P₁V₁^γ = K, then I can use that constant for P₂V₂^γ and obtain the volume, correct?

Exactly.

AM

 

[Nickie]

I would suggest approaching this problem by using the adiabatic process equation, P1V1^γ = P2V2^γ, where γ is the ratio of specific heats (Cp/Cv) for an ideal gas. In this case, since Cv = (5/2)R, then γ = 1.4. From this equation, you can solve for V2 and then use the ideal gas law to solve for T2. Additionally, since the process is adiabatic, Q = 0, so you can use the first law of thermodynamics, ΔU = Q - W, to solve for ΔU and then use the relationship ΔU = ΔH - Δ(PV) to solve for ΔH. Lastly, you can use the work done equation, W = -PΔV, to solve for W. I hope this helps guide you in finding the final temperature and volume.