Kelvin Effect Covers Reading Material in Chapter 10.3 Atmospheric Sciences 5200 Physical Meteorology III: Cloud Physics Vapor Pressure (e)
� < �
Vapor � = � Pressure � > � Relative humidity � �� = � (�)
Supersaturation � > � (�) � ≡ �� − 100% � ≈ 0.5 − 2% in convective updrafts The Clausius-Clapeyron Equation
• Used to find the relationship between pressure and temperature along phase boundaries. The Clausius-Clapeyron Equation
• Used to find the relationship between pressure and temperature along phase boundaries. • Need to derive: • Latent Heat • Gibbs Energy Latent Heat Specific Enthalpy at constant pressure and temperature
Specific Enthalpy – intensive units ℎ ≡ � + �� Mechanical Internal energy work
Constant Pressure � = �ℎ ≡ �� + � �� = �� = �� + ��� � = �
� = (� −� ) + � (� − � ) Latent Heat Specific Enthalpy at constant pressure and temperature
Specific Enthalpy – intensive units ℎ ≡ � + �� Mechanical Internal energy work Constant Temperature �� � = � = �� = �(� − � ) �
� = �(� − � ) Gibbs Energy � = (� −� ) + � (� − � )
� = �(� − � ) Combine (� −� ) + � (� − � ) = �(� − � ) Rearrange Remember Gibbs energy is not � + � � − � � = � + � � − �(� ) constant for temperature and pressure
Gibbs Energy = G = � + � � − � � We assumed isothermal, isobaric change in phase to get G1 = G2 here. Clausius – Clapeyron equation
� �� − s dT = � �� − s dT