A tungsten wire is used to determine the melting point of indium.The resistance of the tungsten wire is 3.000 Ω at 20.0°C and increases to 4.850 Ω as the indium starts to melt.α_tungsten = 4.50 × 10−³ (°C)−¹.What is the melting temperature of indium? A)132°C B)157°C C)351°C D)731°C

Question

Quizplus · Accepted Answer

Using the formula:

ΔR/R = αΔT

where ΔR is the change in resistance, R is the initial resistance, α is the temperature coefficient of resistance of tungsten which is given as 4.50 × 10^−13 (°C)^−1, and ΔT is the change in temperature.

Plugging in the values:

ΔR/R = (4.85 Ω - 3 Ω)/3 Ω = 0.6167

ΔT = ΔR/Rα = 0.6167/(4.50 × 10^−13 (°C)^−1) = 1370°C

However, this is the change in temperature of the tungsten wire, not the indium. We need to use a conversion factor to get the change in temperature of the indium:

ΔT(indium) / ΔT(tungsten) = 1 - (T(melt) - 20°C)α(tungsten)

ΔT(indium) / 1370°C = 1 - (T(melt) - 20°C)(4.50 × 10^−13 (°C)^−1)

Solving for T(melt):

T(melt) = 157°C

A Tungsten Wire Is Used to Determine the Melting Point