Adiabatic processes. ATM60, Shu-Hua Chen

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1 Adiabatic rcesses We can see a simle relatinshi between changes in ressure and temerature fr cases when dq=0, i.e., n heat is added r remved frm the system. As it turns ut, many atmsheric rcesses arximate this situatin. Such a rcess called adiabatic a system underges changes (in ressure, say) but n heat is allwed t enter r leave the system. Examles f rcesses in the atmshere that clsely arximate being adiabatic are: Orgrahic lifting Large scale cnvectin Large scale lifting r subsidence In which mixing r energy exchange with the surrundings ccurs relatively slwly cmared with the seed f the rcess itself. Can yu suggest diabatic rcessed in which dq 0? Pissn s equatin Fr an adiabatic rcess, dq=0 and the first law can be written and, rearranging, 0 = C - d d C The variable f state can be eliminated, using the equatin such that r T RT RT d C R C d 1

2 and, n integratin r ln T ln T R C (ln ln ) T T R / c Fr dry air, R = 287 J/kg/K and C = 1004 J/kg/K S, R C Giving T T This is Pissn s equatin defining hw temerature changes fr a change in ressure during an adiabatic rcess. Ptential temerature, We define the tential temerature f a arcel f air as the temerature that wuld be achieved by bring the arcel dry adiabatically t a ressure f mb. If the initial temerature and ressure f an air arcel were T and, its tential temerature is btained frm Pssin s equatin such that The adiabatic lase rate T is in the unit f mb A lase rate is a rate f decrease f temerature with height (-/dz) either: 1) Observed by an instrument munted n a balln (a radisnde) as it rises thrugh the atmshere, r 2) Exerienced by a arcel f air as it hysically r hythetically rises twards levels f lwer ressure. 2

3 The adiabatic lase rate is the lase rate f a dry arcel f air rising adiabatically thrugh the atmshere. Mre accurately we shuld call this the dry adiabatic lase rate t distinguish it frm a rcess in which cndensatin r evaratin f water drlets is ccurring (the mist r saturated adiabatic lase rate). We can determine the magnitude f the dry adiabatic lase rate by cmbing the hydrstatic equatin and the first law f thermdynamics fr an adiabatic system. The hydrstatic equatin ca be written in terms f either density r secific vlume: d dz g g rearranging this: d gdz Nw, ne frm f the first law f thermdynamics fr an adiabatic rcess (dq=0) is 0 = C - d S, if we substitute fr d, we btain 0 = C - gdz which we can rearrange t becme dz g C Nw, g = 9.81 m s -2, and C = 1004 J kg -1 K -1 thus, dz C / m 9.8 C / km If a arcel f air is lifted in the atmshere such that it des nt exchange energy nr mix with its surrundings, it will decrease in temerature with height at the adiabatic lase rate as calculated. d dz 9.8 C / km 3

4 This is an imrtant reference lase rate fr atmsheric rcesses. Thermdynamic diagrams A diagram n which variatins f the thermal state f a system are shwn is called a thermdynamic diagram. Since the equatin f state relates the three state variables, a system is cmletely secified by any tw f the variables (if yu knw any tw, yu can calculate the third frm the equatin f state). Fr examle, in hysics r engineering, a diagram t study heat engines lts ressure against vlume. On a P-V lt, the wrk dne in a cyclic rcess is reresented by the area enclsed by the curve. In atmsheric science, it is usual t cnstruct diagrams using the tw measured state variables (ressure and temerature). Since ressure changes (decreases) with height, it is ltted n the vertical axis with lwest values at the t and highest values at the bttm. Further, t retain the wrk-area rerty it is necessary t lt the ressure n a lgarithmic scale. This is cnvenient because it makes the vertical axis a nearly linear functin f height. 700 D B F sunding istherm cnstant T ressure lg (/) 800 isbar cnstant C E A Temerature ( C) 4

5 Prcess curves and sunding curves Thermdynamic charts r diagrams are used t dislay bth rcess and sunding curves. The distinctin is imrtant. A rcess curve is a line drawn t reresent a secific rcess such as adiabatic ascent r descent in the atmshere. This culd be a hythetical rcess that we use fr reference urse, r it culd be a rcess that reresents a real event in the atmshere. Many atmsheric rcesses are arximately adiabatic and meterlgical thermdynamic diagram always include adiabats (in the case dry adiabats) fr reference urses. The diagram includes tw dry adiabats (lines AB and CD). A real diagram will include many such lines. Suse a arcel with initial temerature 0 C at the mb level is caused t rise dry adiabatically. As it rises t lwer ressure it will cl at the rate secified by the line AB. Similarly, a arcel lifted frm int C will cl at the rate given by the dry adiabat CD. The adiabats are defined by Pissn s equatin, relating ressure and temerature fr a dry adiabatic rcess T T T is in Kelvin It is cnvenient t label each f the dry adiabats n a diagram accrding t the temerature achieved as each line asses thrugh the ressure level f mb (ints A & C n the diagram). Thus we define the tential temerature f a arcel f air as the temerature that wuld be achieved by bring the arcel dry adiabatically t a ressure f mb. If the initial temerature and ressure f an air arcel were T and, its tential temerature is btained frm Pssin s equatin such that T is in the unit f mb Examle: 5

6 The US standard atmshere (Aendix H f text) lists the temerature and ressure at a height f 5 km t be K (-17.5 C and mb, resectively. The tential temerature f the air at this height is cmuted frm K (31.7 C r 89.1 F) This is the temerature that wuld be achieved if a arcel f air frm 5km were brught dry adiabatically dwn t mb. Ntice that, alng any single dry adiabat, the tential temerature des nt change. Sundings are als ltted n thermdynamic diagrams. An examle is the line EF n the diagram. A sunding is a lt f bservatinal data cllected usually with a radisnde, a balln brne ackage that measures temerature, ressure, and humidity and transmits this data back t the surface as it rises. Radar tracking f the balln als rvides infrmatin n wind seed and directin at heights within the atmshere. A cmarisn f sundings and rcess curves reveals infrmatin abut atmsheric stability. Skew T-lg diagrams Skew-T lg- diagrams are used extensively in meterlgy and the class will have the rtunity t wrk with them during ne f ur discussin grus. The skew T-lg is a mdificatin f the earlier diagram which accmmdates the fact that temerature decreases with height thrugh the trshere. T mre ecnmically use the diagram, the istherms are skewed t the right with increasing height s that sundings and rcess curves are mre vertical (making better use f the aer). Thus, 6

7 sunding ATM60, Shu-Hua Chen 700 istherm ressure lg (/) 800 adiabats 900 isbar Temerature ( C) 7

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