A platinum wire is used to determine the melting point of indium. The resistance of the platinum wire is $2.000 \Omega$ at $20 ^ { \circ } \mathrm { C }$ and increases to $3.072 \Omega$ as indium just starts to melt. What is the melting point of indium? The temperature coefficient of resistivity for platinum is $3.927 \times 10 ^ { - 3 } / \mathrm { C } ^ { \circ }$.
A) $351 ^ { \circ } \mathrm { C }$
B) $156 ^ { \circ } \mathrm { C }$
C) $116 ^ { \circ } \mathrm { C }$
D) $136 ^ { \circ } \mathrm { C }$

Question

Quizplus · Accepted Answer

The melting point of indium can be calculated using the formula for the temperature dependence of resistance: $R = R_0(1 + \alpha \Delta T)$, where $R$ is the final resistance, $R_0$ is the initial resistance, $\alpha$ is the temperature coefficient of resistivity, and $\Delta T$ is the change in temperature. Rearranging to solve for $\Delta T$, we get $\Delta T = \frac{R - R_0}{R_0 \alpha}$. Substituting the given values, $\Delta T = \frac{3.072\Omega - 2.000\Omega}{2.000\Omega \times 3.927 \times 10^{-3}/^\circ C} = 136^\circ C$. Since the initial temperature is $20^\circ C$, the melting point of indium is $20^\circ C + 136^\circ C = 156^\circ C$.

A Platinum Wire Is Used to Determine the Melting Point 2.000Ω2.000 \Omega2.000Ω

A Platinum Wire Is Used to Determine the Melting Point $2.000 \Omega$