- #1

PhilJones

- 9

- 1

## Homework Statement

[/B]

Find the final temperature, Q, ΔU, ΔH given the following

Initial state of gas

T

_{i}= 353K

P

_{i}= 250000Pa

2.5mols of gas

C

_{v}= 12.47Jmol

^{-1}

Final pressure = 125000Pa

## Homework Equations

PV = nRT

W = -PΔV

ΔH = ΔU + Δ(PV)

PV

^{γ}= constant

## The Attempt at a Solution

C

_{v}/ R ≈3/2 so monatomic => γ = 5/2

PV=nRT => V1 = (2.5)(8.314)(325)/(250000) = 0.027 m

^{3}

using PV

^{γ}= constant => V2 = (P1 / P2 *V

^{γ})

^{1/γ}= (2.5/1.25)

^{2/5}* (0.027)= 0.0356 m

^{3}

so T

_{final}= P2 *V2 /(n*R) = [(125000*0.0356)/(2.5*8.314)] = 214K

Q = 0 adiabatic

W = ? nCv ΔT = 2.5*12.47*1(-139) = -4333J?

I get a different answer if I use W = PV

^{γ}* (V2

^{1-γ}- V1

^{1-γ})/(1-γ) = 1527

ΔU = W = -4333J

H = H = ΔU + Δ(PV), should this be = ΔU + nRΔT or = ΔU + PΔV + VΔP? They don't give me the same answer

nRΔT = 2785J, PΔV + VΔP = 5525J but I used P = 125000Pa and V = 0.0356, i don't know if this is the right formula let alone the right parameters to enter.

I didnt even use the fact that the external pressure was 1bar either.

All round confused with this part of my thermal course and just applied random formulas so I think I botched it.

PV

^{γ}= constant is something from another course I did and wasn't in my notes so is it the correct route or maybe an there's an easier method? Any confirmation/corrections would be much appreciated.

Edit: made numerical errors that I corrected

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