Total power of the sun with Rayleigh-Jeans expression

In summary, The total power emitted by the sun over all wavelengths can be calculated by taking the integral of the equation ρt(v)dv=8piv^2kT/c^3 dv, which represents the classical Rayleigh-Jeans expression for ρt(v). This equation gives the power radiated in a range of frequencies and integrating over all possible frequencies will give the total power radiated over the entire spectrum.
  • #1
bhsmith
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0

Homework Statement


What is the totaly power emitted by the sun over all wavelengths (frequencies) according to the (incorrect) classical Rayliegh-Jeans expression for ρt(v)


Homework Equations


ρt(v)dv=8piv^2kT/c^3 dv


The Attempt at a Solution


I'm not sure how to start this one, would i need to take the integral of this equation?
 
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  • #2
bhsmith said:
I'm not sure how to start this one, would i need to take the integral of this equation?

Sounds like a plan to me... (remember, the equation gives the power radiated in a range of frequencies [itex]\nu[/itex] to [itex]\nu+d\nu[/itex], so integrating over all possible frequencies will give the power radiated over the entire spectrum)
 

1. What is the Rayleigh-Jeans expression for the total power of the sun?

The Rayleigh-Jeans expression for the total power of the sun is given by the equation P = 4σT4πR2, where σ is the Stefan-Boltzmann constant, T is the temperature of the sun, and R is the radius of the sun.

2. How is the Rayleigh-Jeans expression used to calculate the total power of the sun?

The Rayleigh-Jeans expression is used to calculate the total power of the sun by taking into account the energy radiated by every point on the surface of the sun and summing it up over the entire surface area of the sun.

3. What is the significance of the Rayleigh-Jeans expression in studying the sun's energy output?

The Rayleigh-Jeans expression is significant in studying the sun's energy output because it provides a mathematical relationship between the sun's temperature and its total power output. This allows scientists to better understand the sun's energy production and predict changes in its output.

4. How does the Rayleigh-Jeans expression differ from the Planck's law?

The Rayleigh-Jeans expression and Planck's law both describe the energy distribution of blackbody radiation, but the Rayleigh-Jeans expression only holds true for low frequencies and high temperatures, while Planck's law accounts for all frequencies and temperatures.

5. Can the Rayleigh-Jeans expression accurately predict the total power of the sun?

No, the Rayleigh-Jeans expression is only an approximation and does not accurately predict the total power of the sun. It fails to account for high frequency radiation and underestimates the sun's energy output. Planck's law provides a more accurate prediction of the sun's total power.

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