# Time for sun's energy

Hello

## Homework Statement

How much time does it take to the sun to furnish an energy of 10 000 KWh on a surface of 31 700 m².

## Homework Equations

Stefan-Boltzman law ?
the power radiated from a black body = σ*T4

## The Attempt at a Solution

I don't know how I can find the time, I don't know any equation that depend on t to find it, if someone can explain me, that would be great !
Thank you !

cepheid
Staff Emeritus
Gold Member
Hmm, so you don't know where time comes in? You know the total energy that must be provided. You also know the power. What is the relationship between energy and power? This will answer your question...

Hello,
Pavg=E/τ ?

cepheid
Staff Emeritus
Gold Member
Yes, generally power = energy/time (power is the RATE at which energy is produced or expended). So, given that information, how would you solve for time?

Also, you are missing one other thing: the Stefan-Boltzman law give you the power radiated PER unit area from a blackbody emitter. So how would you determine the total power radiated in this situation?

t=E/(σ*T4*31700) ?
Thanks

Or I have to use
P=dE/dt
P*dt=dE
∫Pdt=E
∫(σ*T4*31700)dt=E ?
But integrating from what to what ?

cepheid
Staff Emeritus
Gold Member
t=E/(σ*T4*31700) ?

Thanks

Yes.

Or I have to use
P=dE/dt
P*dt=dE
∫Pdt=E
∫(σ*T4*31700)dt=E ?
But integrating from what to what ?

No, you don't have to integrate, because the power is constant with time, so your equation becomes P = dE/dt = ΔE/Δt, and all you have to to is solve for Δt, as you did above.

Ah OK ,
Thank you cepheid !