Adiabatic processes in moist but non-saturated air
Suppose, a unit of non-saturated mass of air get some amount of
energy dq.
dq dud.a. duw.a. dw
dud.a. 1 s cv.d.dTi duw.a. scv.w.dTi
S denotes a fraction of water vapor
сv.a. and сv.a. are specific heat capacities of the dry air and water vapor respectively.
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Pv |
R 1 s |
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R |
s T RT |
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dq 1 s c |
sc |
dT Pdv |
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v.d. |
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v.w. |
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Equation of state for moist, non- |
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Pdvi |
Rc 1 s Rws dTi |
vidP |
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saturated air |
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dP |
cv R cp |
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dq 1 s c |
sc |
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RT |
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i |
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dT R 1 s R s dT v dPi |
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v.d. |
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v.w. |
i c |
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w |
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P |
vi |
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RT |
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P |
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dq 1 s cp. scp dTi RTi |
dP |
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21 |
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P |
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Rc |
287 |
J kg K |
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cp.d 1005 J kg K |
cp.w 1864 J kg K |
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R |
461 J |
kg K |
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cv.d. 718 |
J |
kg K |
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J kg K |
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w |
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cv.w. 1409 |
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1 0,04 1005 0,04 1864 1039 J |
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smax 0,04 |
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kgK |
cp.m. |
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For practical purposes |
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9,81 |
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0,95 K |
100m |
1K |
100m |
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cp.m |
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we may adopt |
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1039 |
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R R 287 J |
kgK |
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R 1 0,04 287 0,04 461 294 J |
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c |
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kgK |
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cp cp.d 1005 J |
kgK |
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Conclusion |
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At adiabatic ascent, the temperature of a moist, non-saturated parcel of air varies, practically, in the same way as a dry parcel does.
The dry adiabat is a curve of state for the moist, non-saturated air too.
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