Chapter Ten - Major Applications: Hurricanes and Global Warming

what is the importance of hurricanes

they transport the earths energy from the equator to the poles

what is the AB leg of the hurricane carnot engine

AB - dry air becomes moist as water absorbed Qvap from warm sea and turns into vapour at a constant temp Tss

what is the BC leg of the hurricane carnot engine

moist air at the storm centre is less dense and rises adiabatically to the tropopause

what is CD leg of the hurricane carnot engine

the moist air deposits Q’ isothermally as water vapour turns into water and the air dries

what is the DA leg of the hurricane carnot engine

the dry air is denser and adiabatically compresses as it sinks towards the ground again completing one cycle

what happens work in a hurricane carnot cycle

the work extracted is manifested as air kinetic energy

mathematically what is happening in the AB process for hurricane carnot cycle

initially the water is liquid but turns to vapour as the parcel travels inwards, this expands as the water vaporises, the expansion is isothermal as the sea is constant T reservoir so change in U of the air and water parcel = Qv - Pchange in V so Qv = change in U + P change in V where Qv is the heat supplied by the sea to vaporise the water (latent heat of vaporisation)

what is the humidity of the incoming parcel of dry air

w = mw/ md where mw is mass of water in liquid or vapour form and md is mass of dry air

what is the equation for mixing ratio of parcel of air entering hurricane

w0 = mw0/md where mw0 is initial mass of water

what is w after absorbing mass mw of water

w = mw0 + mw/md = w0 + mw/md

so what is heat needed to vaporise water

amount of vaporised water is mw = (w- w0)md so Qv = mwchange in hv = (w-w0)mdchnagein hv where change in hv is specific enthalpy of vaporisation of water

what is work extracted from ideal hurricane

Qv - Q’ = W

what is the upper limit for W

W < or equal to (1 - Ttr/Tss)Qv

what does the upper limit for W neglect

feedback caused by energy of wind being dissipated as heat in wind surface interaction which contributes to the heat of the incoming air

what is limit for W taking feedback into account

W < or equal to [Tss/Ttr] x (1-Ttr/Tss)Qv

how is limit for W including feedback derived

assuming all the W reappears as heat input then total heat exchange is Q1 = Qv + W and so Q1 - Q’ = W, so W < or equal to ( 1- Ttr/Tss)Q1 which can be subbed with equation for Q1 to give eqn

what is the differential form of the limit to work

W’ < or equal to (Tss-Ttr/Ttr) Qv’

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