Question 24

At room temperature $$(27°C)$$, the resistance of a heating element is $$50\Omega$$. The temperature coefficient of the material is $$2.4 \times 10^{-4} \text{ °C}^{-1}$$. The temperature of the element, when its resistance is $$62\Omega$$, is ______ °C.

Correct Answer: 1027

$$R = R_0(1+\alpha\Delta T)$$. $$62 = 50(1+2.4\times10^{-4}(T-27))$$.

$$1.24 = 1 + 2.4\times10^{-4}(T-27)$$.

$$0.24 = 2.4\times10^{-4}(T-27)$$.

$$T-27 = 1000 \implies T = 1027$$°C.

The answer is $$\boxed{1027}$$.

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