By Anastasios Tsonis
Textbook for brief undergraduate classes in atmospheric technological know-how, meteorology, physics or average technology courses.
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Additional resources for An Introduction to Atmospheric Thermodynamics
Since there was no temperature change and no variation in energy during the process we must conclude that a variation in volume at a constant temperature produces no variation in energy. In other words U = f (V ) which means that U is only a function of T : U = U (T ). 2 you will be asked to prove this mathematically. 16), (∂U/∂T )V = dU/dT . 17) cV = du . 18) cp = dh . dT In the atmospheric range of temperatures, cV and cp are nearly constant. 17) we then have that U= CV dT + constant or U = CV T + constant.
As such a polytropic process pV η = constant reduces to an isobaric, to an isothermal, to an adiabatic, and to isochoric process for η = 0, 1, γ, and ∞, respectively. Having said this we must add that in the atmosphere over a rather wide range of motions the timescale for an air parcel (our system) needed to adjust to environmental changes of pressure, and to perform work, is short compared with the corresponding timescale of heat transfer. For example, above the boundary layer and outside the clouds the timescale of heat transfer is about two weeks whereas the timescale of displacements that aﬀect a parcel is of the order of hours to a day.
1 The shaded area gives the work done when a system changes from an initial state i to a final state f . 2 The shaded area gives the work done during a cyclic reversible transformation. f pdV i Vf V p f 1 W = Ai1f 2i i 2 Vi V Vf from f to i along exactly the same path in the (p, V ) diagram. Then, the total work done will be f W = i pdV + i f f f pdV − pdV = i pdV = 0. 2) f i pdV W = i + 1 pdV f 2 = area under curve 1 − area under curve 2 = Ai1f 2i = 0 where Ai1f 2i is the area enclosed by the two paths.
An Introduction to Atmospheric Thermodynamics by Anastasios Tsonis