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

## 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