A red giant star radiates a power of 2.0 × 10²⁹ W from a surface at 3500 K…

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A red giant star radiates a power of $2.0 \times 10^{29}\ \text{W}$ from a surface at $3500\ \text{K}$ . Treating it as a black body, find its radius, and compare it with the Sun's, $6.96 \times 10^{8}\ \text{m}$ . ( $\sigma = 5.67 \times 10^{-8}\ \text{W m}^{-2}\text{K}^{-4}$ .)

Need a reminder? The key ideaShow

Radiation: $P = e\sigma AT^4$ , net $e\sigma A(T^4 - T_0^4)$ , with $\sigma = 5.67 \times 10^{-8}\ \text{W m}^{-2}\text{K}^{-4}$ and $T$ in kelvin. Wien: $\lambda_mT = 2.90 \times 10^{-3}\ \text{m K}$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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