How Long Would It Take for Earth to Reach 100°C?

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Homework Help Overview

The problem involves calculating the time it would take for the Earth to reach a temperature of 100°C from 0°C, given the amount of radiant energy it receives from the Sun and assuming it is composed entirely of water. The context is rooted in thermodynamics and energy transfer.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of the formula Q=cmT to determine the energy required to heat the water and consider dividing this by the intercepted energy from the Sun. There are questions about the correct values and units to use in the calculations.

Discussion Status

Some participants have attempted calculations but express uncertainty about their results. There is a suggestion to verify the formulas studied in class, and one participant points out a potential error in the specific heat capacity value used, indicating a focus on unit accuracy.

Contextual Notes

Participants are working under the assumption that no energy is lost to radiation or reflection, which may not reflect real-world conditions. There is also a lack of clarity on the specific heat capacity value and its units, which is critical for the calculations.

intenzxboi
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Homework Statement



The Earth intercepts 1.27 ´ 1017 W of radiant energy from the Sun. Suppose the Earth, of volume 1.08 ´ 1021 m3, was composed of water. How long would it take for the Earth at 0°C to reach 100°C, if none of the energy was radiated or reflected back out into space?

no clue how to start.
what formulas are related to this problem
 
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intenzxboi said:
no clue how to start.
what formulas are related to this problem

What formulas has your class studied recently? I would look at those.
 
I'm not entirely sure either. But using Q=cmT to find out the energy needed to heat the water, and then dividing by the intercepted energy.

Q=4x(1.08x10^26)x100

=4.32x10^26

Then divide by the intercepted power. Which converts to J/s.

The answer comes out wrong though.
 
You used the wrong value of c. Hint: pay attention to units.
 

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