Wallace and Hobbs 2.5 – Adiabatic Processes

by Joe Archive on August 4, 2008

2.5 Adiabatic Processes – changes of state (pressure, volume, temperature) without heat added to or lost from the system.br /br /eg. Adiabatic compression of a gas – compression does work so the internal energy of the system increases, raising the temperature. This temperature is higher than that that the system would have if it was compressed isothermally, so the resulting pressure is also higherbr /br /2.5.1 Air Parcelsbr /br /When considering vertical motion and mixing of air, it is often useful to consider the behaviour of a “parcel” – an infinitesimal volume of gas that is: thermally insulated from the environment, stays at the same pressure as its surrounds and is moving infinitesimally slowly, so that KE is negligible.br /br /2.5.2 Adiabatic Lapse ratebr /br /Consider a parcel lifted (or depressed) in the atmosphere, adhering to the assumptions above – how does its temperature vary with height?br /br /Assuming a hydrostatic atmosphere and only adiabatic processes only, the parcels will satisfy:br /blockquotebr /d(c_pT + Phi) = 0br /br /c_p dT/dz = -dPhi/dzbr /br /Gamma = -dT/dz = g/c_p = 9.8 deg/km/blockquotebr /br /dry adiabatic lapse rate.br /br /2.5.3 Potential Temperaturebr /br /theta is defined as the temperature a parcel would have if it was adiabatically moved from its present environment to a reference pressure level (usually sea level/1000mb)br /br /From the first law:br /br /blockquotec_pdT – alpha dp = 0/blockquotebr /br /using the ideal gas law,br / br /blockquotec_p/R dT/T = dp/p/blockquotebr /br /or, integrating from the reference level to the present level,br /br /blockquote(c_p/R)ln(T/theta) = ln(p/p0)/blockquotebr /br /or br /br /blockquotetheta = T(p_0/p)^(R/c_p)/blockquotebr /br /Under adiabatic processes, the potential temperature of a parcel is conserved.br /br /2.5.4 – The pseudoadiabatic chartbr /br /The potential temperature lends itself to graphical solution. See charts in WHbr /br /Example 2.6 – a parcel at 400mb has a temperature of 230K – what will be its temperature if it is moved adiabatically to 600mb?br /br /Reference to charts (or calculation) shows that this parcel has a potential temperature of 300K. It will still have this theta at its final position. Reversing the calculation, or again referring to the chart shows that the parcel now has a temperature of 260K

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