What is the approximate temperature of the outer core and the lower mantle?
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As the outer core is fluid and presumably convecting (and with an additional correction for the presence of impurities in the outer core), we can extrapolate this range of temperatures to a temperature at the base of Earth's mantle (the top of the outer core) of roughly 3,500 to 5,500 kelvins (5,800 to 9,400 degrees F) at the base of the earth's mantle.
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