(b) $t_{n} = \frac{\alpha}{\beta} = \left( \frac{500}{5} \right) = 100℃$ Also$\ t_{n} = \frac{t_{i} + t_{c}}{2} \Rightarrow 100 = \frac{t_{i} + 0}{2} \Rightarrow t_{i} = 200℃$
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Ph.D. in Physics with 19+ years of teaching experience.