Resistivity and temperature: A platinum wire is used to determine the melting point of indium. The resistance of the platinum wire is 2.000 Ω at 20°C and increases to 3.072 Ω as the indium starts to melt. What is the melting point of indium? The temperature coefficient of resistivity for platinum is 3.9 × 10^-3(C°)^-1.

Question

Quizplus · Accepted Answer

We can use the formula for resistivity and temperature relationship:
R = ρL/A
where R is resistance, ρ is resistivity, L is length, and A is cross-sectional area.

We can rearrange this to solve for resistivity:
ρ = RA/L

Next, we can use the temperature coefficient of resistivity to calculate the change in resistivity from 20°C to the melting point of indium:
Δρ = ραΔT
where α is the temperature coefficient and ΔT is the change in temperature.

We can set up two equations based on the resistivity of the wire at two different temperatures:
ρ1 = R1A/L
ρ2 = R2A/L

And we can use the change in resistivity to set up another equation:
Δρ = ρ2 - ρ1 = ρ1αΔT

We can eliminate A/L from these equations by dividing them:
ρ2/ρ1 = R2/R1

Solving for ΔT, we get:
ΔT = (R2/R1 - 1)/α

Plugging in the given values, we get:
ΔT = (3.072/2.000 - 1)/(3.9 × 10-3 × 100) = 160°C

Therefore, the melting point of indium is:
20°C + ΔT = 20°C + 160°C = 180°C

The closest answer choice is C) 160°C.

Resistivity and Temperature: a Platinum Wire Is Used to Determine