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

AI Thread Summary
To determine how long it would take for Earth to reach 100°C from 0°C using the intercepted solar energy, the relevant formula is Q=cmT, where Q is the heat energy required, c is the specific heat capacity of water, m is the mass of the Earth, and T is the temperature change. The total energy needed to heat the Earth, treated as water, is calculated as Q=4x(1.08x10^26)x100, resulting in 4.32x10^26 J. This value should then be divided by the intercepted power of 1.27 x 10^17 W to find the time in seconds. Attention to units is crucial for accurate calculations, as incorrect values can lead to erroneous results. Proper application of these formulas will yield the correct time estimate for the temperature increase.
intenzxboi
Messages
98
Reaction score
0

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
 
Physics news on Phys.org
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.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

How Long for a Beam of Light to Reach Earth?
Replies
21
Views
1K
Calculating Time to Heat Earth to 100°C
Replies
1
Views
2K
How Long Would It Take for Earth's Temperature to Rise from 20°C to 90°C?
Replies
18
Views
6K
Calculate the Average Surface Temperature of Earth
Replies
7
Views
5K
How Long Would It Take for a Water-Composed Earth to Heat from 40°C to 90°C?
Replies
2
Views
2K
How to calculate freezing time for a moist food by-product (75% water)
Replies
6
Views
691
Heat transfer, how long it takes ice to reach melting point
Replies
6
Views
4K
Temperature as a function of time in black body radiation
Replies
14
Views
2K
Solar Panels and Solar Radiation Flux Density Help - Very Confused
Replies
35
Views
5K
Thermodynamics: Internal Energy, Heat and Work Problem
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top