8.6.10+Solve+Cal

=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 <span style="font-family: Georgia,serif;"> A = area in m^2 <span style="font-family: Georgia,serif;"> T = absolute temperature in K <span style="font-family: Georgia,serif;"> I = Intensity <span style="font-family: Georgia,serif;"> P = Power

<span style="font-family: Georgia,serif;"> I = P / A = σT^4 <span style="font-family: Georgia,serif;"> 220 W m^-2 = (5.67 x 10^-8 W m^-2 K^-4)(T^4) <span style="font-family: Georgia,serif;">T^4 = 3.88 x 10^9 <span style="font-family: Georgia,serif;">T = 250 K = -23 ºC

<span style="font-family: Georgia,serif;">(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. <span style="font-family: Georgia,serif;">∆V = ßV∆T <span style="font-family: Georgia,serif;">∆V = increase in volume <span style="font-family: Georgia,serif;">ß = coefficient of volume expansion <span style="font-family: Georgia,serif;">V = the original volume <span style="font-family: Georgia,serif;">∆T = temperature change

<span style="font-family: Georgia,serif;">∆V = (2.0 x 10^-4 K^-1)(2.5 x 10^6 km^2)(1.5 km)(3.5 K) = 2625 km^3 <span style="font-family: Georgia,serif;">rise in sea level = 2625 km^3 / 2.5 x 10^6 km^2 = 0.00105 km = 1.05 m

<span style="font-family: Georgia,serif;">Reminder: <span style="font-family: Georgia,serif;">Specific Heat Capacity: <span style="font-family: Georgia,serif;">c = Q / (m∆T)

<span style="font-family: Georgia,serif;">Latent Heat: <span style="font-family: Georgia,serif;">L = Q / m