# 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 $L=25$ cm and a cross-sectional diameter $D=1$ mm heat up if a voltage $U=220$ V is applied to its ends and a current $I=5$ A flows through the wire for a long time?

## Answer: 2229 K
# 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:

$$
\sigma T^{4} L \cdot \pi D=U I \text {. Therefore: } T=\sqrt[4]{\frac{U I}{L \pi D}}=\sqrt[4]{\frac{220 \cdot 5}{5.67 \cdot 10^{-8} \cdot 0.25 \cdot 3.14 \cdot 1 \cdot 10^{-3}}}=2229 \mathrm{~K}
$$