We’ve seen that it takes about 1031 J to melt the entire mantle. Let’s calculate how long this magma ocean remains liqui
Posted: Wed May 04, 2022 1:24 pm
We’ve seen that it takes about 1031 J to melt the entire mantle.
Let’s calculate how long this magma ocean remains liquid. We’ll
make some radically simplifying assumptions: Energy radiates from
the surface as a black body and there is no atmosphere.
Furthermore, the magma ocean solidifies from the base towards the
surface, and heat is carried to the surface rapidly. Step 1: Draw a
schematic of the problem. Step 2: Black body radiation radiates
energy away from a surface at the rate of sT4, where s is the
Stephan-Boltzmann constant, 5.67x10-8 W/m2/K4 (a watt is J/s)
Approximately how long will it take the magma ocean to emit 1031 J
of energy? Assume the temperature of a magma at the surface is
~2000 K. Express you answer in years (1 year is 3.15 x 107 s). You
should get an answer more than a year, but less than the age of the
Earth. To do this problem, think carefully about units to address
missing information. Draw a picture if you are struggling to start.
Step 3: Add to your picture in a different color the consequences
of one or two of the simplifying assumptions (e.g. add an
atmosphere, the solidification occurs at the surface or mid-mantle,
or the radiation occurs as a grey body) and discuss in words how
you think it will change the cooling time of the magma
ocean.
Let’s calculate how long this magma ocean remains liquid. We’ll
make some radically simplifying assumptions: Energy radiates from
the surface as a black body and there is no atmosphere.
Furthermore, the magma ocean solidifies from the base towards the
surface, and heat is carried to the surface rapidly. Step 1: Draw a
schematic of the problem. Step 2: Black body radiation radiates
energy away from a surface at the rate of sT4, where s is the
Stephan-Boltzmann constant, 5.67x10-8 W/m2/K4 (a watt is J/s)
Approximately how long will it take the magma ocean to emit 1031 J
of energy? Assume the temperature of a magma at the surface is
~2000 K. Express you answer in years (1 year is 3.15 x 107 s). You
should get an answer more than a year, but less than the age of the
Earth. To do this problem, think carefully about units to address
missing information. Draw a picture if you are struggling to start.
Step 3: Add to your picture in a different color the consequences
of one or two of the simplifying assumptions (e.g. add an
atmosphere, the solidification occurs at the surface or mid-mantle,
or the radiation occurs as a grey body) and discuss in words how
you think it will change the cooling time of the magma
ocean.