Troposphere Lapse rate and The Stratosphere (3.1-3.2)

lapse rate

The rate at which temperature decreases with an increase in altitude.

Equations involved in the lapse rate equation

Hydrostatic pressure, 1st law of thermodynamics, enthalpy, entropy, ideal gas

Entropy equation

Tds = dh - vdp

Enthalpy equation

h = u +pv

Ideal Gas Equation

PV=nRT, V = 1/rho

hydrostatic pressure in a column of air

dp / dz = -(rho)g

Dry Adiabatic Lapse Rate

The rate at which the temperature of a parcel of dry air decreases as the parcel is lifted in the atmosphere.

lapse rate equation

dT / dz = -g / cp

What does the temperature of air as it rises in elevation depend on?

specific heat (more specifically, the negative of gravity over specific heat)

geopotential elevation

The 'elevation' used in equations if gravity is not changed with elevation (if sea level gravity is used)

geopotential elevation equation

z(h) = (integral from 0 to h) (g/go) dh'

Lambda

another way to describe lapse rate, -go / cp

Variation of temperature in the troposphere equation

p(z) = po(1+([lamdba]z/To))^(-go/[lambda]R)

How does air temperature change with height in the troposphere?

It decreases

How does air change with height in the stratosphere?

It decreases

What is absorbed in the stratosphere?

Harmful UV rays

Why does the air temperature go up with increasing altitude in the stratosphere?

Ozone layer absorbs high energy UV radiation from the sun

What is the ozone molecule?

O3

Chapman Cycle

the first set of natural steady-state chemical reactions proposed for stratospheric ozone

Chapman cycle first step

Oxygen molecules absorbed UV-C photons and split into oxygen atoms, O2 + 2(pi)hv [wavelength of 242 nm] -> O + O

Chapman cycle second step

An oxygen atom from the first step combines with an oxygen molecule and release the excess energy (originally from the UV-C photon) to the neighboring oxygen or nitrogen molecules (M), thereby heating those up, O + O2 + M -> O3 + M

Chapman cycle third step

The ozone molecule dissociates upon absorbing longer wavelength (UV-(B,C)) rays, resulting again in an oxygen atom, O3 + 2(pi)hv [wavelength of 242 to 310 nm] -> O + O2

Chapman cycle fourth step

The oxygen atom from the third step can combine with another oxygen molecule to form a new ozone molecule, releasing additional thermal energy to the surrounding oxygen and nitrogen molecules (just like step 2)

How fast do chapman cycle chemical reactions cycle?

Fast, ozone molecules are quickly destroyed but created quick enough that a layer of them exists

What reaction ultimately destroys Ozone?

O3 + O -> 2O2