By David G. Andrews
A quantitative creation to the Earth's surroundings for intermediate-advanced undergraduate and graduate scholars, with an emphasis on underlying actual rules. This variation has been introduced thoroughly up to date, and now features a new bankruptcy at the physics of weather swap which builds upon fabric brought in previous chapters, giving the scholar a huge figuring out of a few of the actual strategies underlying this most vital and topical topic. not like many different books on atmospheric technological know-how, the emphasis is at the underlying physics. Atmospheric purposes are built commonly within the difficulties given on the finish of every bankruptcy. The ebook is an important source for all scholars of atmospheric physics as a part of an atmospheric technological know-how, meteorology, physics, Earth technological know-how, planetary technology, or utilized arithmetic direction.
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Extra resources for An Introduction to Atmospheric Physics, Second Edition
11 Atmospheric thermodynamics A schematic plot of the Gibbs free energy G as a function of the droplet radius, for RH = e/es = 90% and 110%. 57). e > es (T) (indicating supersaturated conditions), then the logarithm is positive, β > 0, and there is a maximum of G at a radius a given by a= 2α 2γ = . 57) This is known as Kelvin’s formula; it may also be written in the form e = es (T) exp A a where A = 2γ . 58) A well-known thermodynamic result is that a system at constant temperature and pressure tends to evolve in such a way that its Gibbs free energy decreases;13 stable equilibrium is attained when the Gibbs free energy is a minimum.
A droplet of this size is unlikely to form by random collisions of smaller droplets, so a more viable process is for the droplet to condense on a small pre-existing solid or liquid particle, known as a cloud condensation nucleus. The above theory must be modiﬁed signiﬁcantly if solutes are present in the cloud droplet. Raoult’s law states that, over a droplet containing N moles of solute and N0 moles of pure water, the vapour pressure must be modiﬁed by the factor φ =1− N N0 if N N0 . Consider a spherical droplet of radius a and volume Va = 4π a3 /3 containing a mass m of solute of molar mass M.
4 again. If = a we have neutral stability. As a further step, we can investigate the buoyancy force on the parcel and its acceleration. e. gV1 ρe1 − ρp1 at height z1 , where V1 is the volume of the parcel there. e. ρp1 V1 d 2 (δz) . dt2 We therefore have Tp1 ρe1 d 2 (δz) =g −1 =g −1 ρp1 Te1 dt2 =g =− T− T− g ( T a a δz δz −1 =g − a T − δz δz − ) δz to leading order in the small quantity δz. 31) is that of the environment. 30) represents simple harmonic motion, with sinusoidal solutions. 7). 30), one of which corresponds to the displaced parcel continuing to move at an increasing speed.