- #1

whitebuffalo

- 2

- 0

**Homework Statement**

Cloud moves from alt. 2000m (P = 0.802atm) to 3500m (P = 0.602) when it encounters a mountain. It expands adiabatically. The initial temp is 288K, C

_{P,m}for the air is 28.86 J/Kmol (assume ideal). What is the final temp and will it drop it's moisture?

**The attempt at a solution**

This is what I did. C

_{V,m}= C

_{P,m}- R

C

_{V,m}dT = -[tex]\frac{RT}{V}[/tex]dV

[tex]\int[/tex]C

_{V,m}dT = [tex]\int[/tex]-[tex]\frac{RT}{V}[/tex]dV divide by T

C

_{V,m}[tex]\int[/tex][tex]\frac{1}{T}[/tex]dT = -R[tex]\int[/tex][tex]\frac{1}{V}[/tex]dV

C

_{V,m}ln([tex]\frac{T2}{T1}[/tex]) = R ln([tex]\frac{V1}{V2}[/tex]) rearrange

T2 = T1(V1/V2)

^{R/CV,m}this to solve for T2, but 2 variables, so...

P

_{1}V

_{1}

^{[tex]\gamma[/tex]}= P

_{2}V

_{2}

^{[tex]\gamma[/tex]}solve for the ratio V1/V2

[tex]\frac{V1}{V2}[/tex] = ([tex]\frac{P2}{P1}[/tex])

^{1/[tex]\gamma[/tex]}

T2 = T1 (([tex]\frac{P2}{P1}[/tex])

^{1/[tex]\gamma[/tex]})

^{R/CV,m}

C

_{V,m}= C

_{P,m}- R = 20.546 [tex]\gamma[/tex] = C

_{P,m}/C

_{V,m}= 1.405

T2 = 288 (([tex]\frac{0.602}{0.802}[/tex])

^{1/1.405})

^{8.314/20.546}= 265K

Someone please tell me if I did this right, if not, what did I do wrong..........and how do I know if it will drop moisture?

This is my first HW question in Pchem I and only the 2nd week of the semester, so please explain anything so I can understand it.

Last edited: