Whaaa Calculating the temperature of the suns surface

AI Thread Summary
Calculating the temperature of the sun's surface involves analyzing the solar spectrum and using the formula (hf^3)/((e^(hf/Kb T))-1). The key steps include differentiating this formula, calculating the frequency corresponding to the most common photon energy of 1.15 eV, and solving for zero. The user is struggling with the differentiation process, as their calculator fails to identify the zero points. Seeking assistance, they reference Wien's Displacement Law for further context. Accurate differentiation is crucial for determining the sun's surface temperature effectively.
Lisa...
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Hi you all!

I'm having difficulties with estimating the temperature of the surface of the sun from a given solar spectrum. I've already determined the photon energy of the most common photons (1.15 eV). I also know that the curve of the solar spectrum (photon energy on the x-axis and intensity on the y-axis) is described with (hf^3)/((e^(hf/Kb T))-1) where the frequency f corresponding to 1 eV energy is 2.417970 x 10^14 Hz.

Now the way to retrieve the correct answer is the following:
1) Differentiate the formula.
2) Calculate the frequency of the most common photons and fill that in the formula.
3) Solve the equation where the differentiated formula (with f filled in) is set zero. (This may be done with a graphic calculator)

The only problem is that I don't seem to differentiate the formula correctly, because my calculator just can't find the points where it's zero. Could someone pleaaaaaaaaaaaaaaaaase help me to differentiate it the right way?o:)
 
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Thread 'Variable mass system : water sprayed into a moving container'

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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}...
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