# Problem No. 8 (10 points)

It is known that a heated body radiates energy from one square meter each second, which is determined by the expression $w=\sigma T^{4}$, where $\sigma=5.67 \cdot 10^{-8}$ J $/(c \cdot \mu^{2} \cdot K^{4})$. To what temperature will a piece of wire with a length of $L=50$ cm and a cross-sectional diameter of $D=2$ mm heat up if a voltage of $U=220$ V is applied to its ends and a current of $I=5$ A flows through the wire for a long time?

## Answer: $1576 \mathrm{~K}$

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# Solution and Evaluation Criteria:

Power of the current flowing through the wire: $P=U I$.

Power of thermal radiation: $P=w \cdot S=\sigma T^{4} L \cdot \pi D$

We obtain:

$\sigma T^{4} L \cdot \pi D=U I$. From which: $T=\sqrt[4]{\frac{U I}{L \pi D}}=\sqrt[4]{\frac{220 \cdot 5}{5.67 \cdot 10^{-8} \cdot 0.5 \cdot 3.14 \cdot 2 \cdot 10^{-3}}}=1576 \mathrm{~K}$

![](https://cdn.mathpix.com/cropped/2024_05_06_dde97d69ac546735bb46g-06.jpg?height=345&width=363&top_left_y=176&top_left_x=158)

Multidisciplinary Engineering Olympiad "Star" in Natural Sciences

## Final Stage

2016-2017 academic year

## Problems, Answers, and Evaluation Criteria

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