Global warming


8.6.10 Solve problems related to the enhanced greenhouse effect.

(1) A researcher uses the following data for a simple climatic model of a planet without an atmosphere.
Data:
Incident solar radiation = 350 W m^-2
Absorbed solar radiation = 220 W m^-2
(a) Determine the average albedo for the planet used in the modeling.
albedo = (total scattered power) / (total incident power)
1 - 220 / 350 = .37 = 37%

(b) Determine the intensity of the outgoing radiation.
Intensity In = Intensity Out
220 W m^-2 = 220 W m^-2

(c) Estimate the temperature of the planet, assuming constant.
Stefan-Boltzmann Law
power = σAT^4
σ = Stefan-Boltzman constant = 5.67 x 10^-8 W m^-2 K^-4
A = area in m^2
T = absolute temperature in K
I = Intensity
P = Power

I = P / A = σT^4
220 W m^-2 = (5.67 x 10^-8 W m^-2 K^-4)(T^4)
T^4 = 3.88 x 10^9
T = 250 K = -23 ºC

(2) The area of the Mediterranean sea is approximately 2.5 x 10^6 km^2 and the average depth is about 1.5 km. Using a coefficient of volume expansion of water of 2.0 x 10^-4 K^-1, estimate the expected rise in sea level after a temperature increase of 3.5 K.
∆V = ßV∆T
∆V = increase in volume
ß = coefficient of volume expansion
V = the original volume
∆T = temperature change

∆V = (2.0 x 10^-4 K^-1)(2.5 x 10^6 km^2)(1.5 km)(3.5 K) = 2625 km^3
rise in sea level = 2625 km^3 / 2.5 x 10^6 km^2 = 0.00105 km = 1.05 m

Reminder:
Specific Heat Capacity:
c = Q / (m∆T)

Latent Heat:
L = Q / m