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whitebuffalo
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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, CP,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. CV,m = CP,m - R
CV,mdT = -[tex]\frac{RT}{V}[/tex]dV
[tex]\int[/tex]CV,mdT = [tex]\int[/tex]-[tex]\frac{RT}{V}[/tex]dV divide by T
CV,m[tex]\int[/tex][tex]\frac{1}{T}[/tex]dT = -R[tex]\int[/tex][tex]\frac{1}{V}[/tex]dV
CV,mln([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...
P1V1[tex]\gamma[/tex] = P2V2[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
CV,m = CP,m - R = 20.546 [tex]\gamma[/tex] = CP,m/CV,m = 1.405
T2 = 288 (([tex]\frac{0.602}{0.802}[/tex])1/1.405)8.314/20.546 = 265KSomeone 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.
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, CP,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. CV,m = CP,m - R
CV,mdT = -[tex]\frac{RT}{V}[/tex]dV
[tex]\int[/tex]CV,mdT = [tex]\int[/tex]-[tex]\frac{RT}{V}[/tex]dV divide by T
CV,m[tex]\int[/tex][tex]\frac{1}{T}[/tex]dT = -R[tex]\int[/tex][tex]\frac{1}{V}[/tex]dV
CV,mln([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...
P1V1[tex]\gamma[/tex] = P2V2[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
CV,m = CP,m - R = 20.546 [tex]\gamma[/tex] = CP,m/CV,m = 1.405
T2 = 288 (([tex]\frac{0.602}{0.802}[/tex])1/1.405)8.314/20.546 = 265KSomeone 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.
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