Osmium wire

A spiral of osmium wire has a resistance of 300 ohms at a temperature of 20 degrees Celsius. To what temperature was the coil heated if its resistance rose to 2940 ohms? (alpha=4*10^-3 1/K)

Correct answer:

t₂ =  2220 °C

Step-by-step explanation:

$$\begin{gathered} t_1=20\text{°C} \\ {R}_1=300\Omega \\ {R}_2=2940\Omega \\ \alpha =4\cdot 10^{-3}=0.0041\text{/K} \\ {R}_2=R_1\cdot (1+\alpha \cdot (t_2-t_1)) \\ {R}_2/R_1-1=\alpha \cdot (t_2-t_1) \\ {t}_2=\frac{R_2/R_1-1}{\alpha }+t_1=\frac{2940/300-1}{0.004}+20=2220\text{°C} \end{gathered}$$

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