How long does it take for the sun to produce 10,000 KWh on a 31,700 m² surface?

[Dassinia]

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-Boltzmann 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]

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...

 

[Dassinia]

Hello,
P_avg=E/τ ?

 

[cepheid]

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-Boltzmann 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?

 

[Dassinia]

t=E/(σ*T⁴*31700) ?
Thanks

 

[Dassinia]

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]

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.

 

[Dassinia]

Ah OK ,
Thank you cepheid !