A resistance thermometer, which measures temperature by measuring the change in resistance of a conductor, is made from platinum and has a resistance of 50.0 Ω at 20.0°C. When immersed in a vessel containing melting indium, its resistance increases to 76.8 Ω. Calculate the melting point of the

Question

A resistance thermometer, which measures temperature by measuring the change in resistance of a conductor, is made from platinum and has a resistance of 50.0 Ω at 20.0°C. When immersed in a vessel containing melting indium, its resistance increases to 76.8 Ω. Calculate the melting point of the indium.

Accepted Answer

Solving Equation 27.21 for ΔT and using the α value for platinum given in Table 27.1, we obtain

[latex] R=R_{0}\left[1+\alpha\left(T-T_{0} ight) ight] [/latex] (27.21).

[latex] \Delta T=\frac{R-R_{0}}{\alpha R_{0}}=\frac{76.8 \Omega-50.0 \Omega}{\left[3.92 imes 10^{-3}\left({ }^{\circ} C ight)^{-1} ight](50.0 \Omega)} [/latex].

[latex] =137^{\circ} C [/latex].

[latex] ext { Because } T_{0}=20.0^{\circ} C [/latex], we find that T, the temperature of the melting indium sample, is 157.C.

Table 27.1
Resistivities and Temperature Coefficients of Resistivity for Various Materials
Temperature Coefficient [latex]\alpha\left[\left({ }^{\circ} C ight)^{-1} ight][/latex]	Resistivity (Ω(m)	Material
[latex]3.8 imes 10^{-3}[/latex]	[latex]1.59 imes 10^{-8}[/latex]	Silver
[latex]3.9 imes 10^{-3}[/latex]	[latex]1.7 imes 10^{-8}[/latex]	Copper
[latex]3.4 imes 10^{-3}[/latex]	[latex]2.44 imes 10^{-8}[/latex]	Gold
[latex]3.9 imes 10^{-3}[/latex]	[latex]2.82 imes 10^{-8}[/latex]	Aluminum
[latex]4.5 imes 10^{-3}[/latex]	[latex]5.6 imes 10^{-8}[/latex]	Tungsten
[latex]5.0 imes 10^{-3}[/latex]	[latex]10 imes 10^{-8}[/latex]	Iron
[latex]3.92 imes 10^{-3}[/latex]	[latex]11 imes 10^{-8}[/latex]	Platinum
[latex]3.9 imes 10^{-3}[/latex]	[latex]22 imes 10^{-8}[/latex]	Lead
[latex]0.4 imes 10^{-3}[/latex]	[latex]1.50 imes 10^{-6}[/latex]	Nichrome
[latex]-0.5 imes 10^{-3}[/latex]	[latex]3.5 imes 10^{-5}[/latex]	Carbon
[latex]-48 imes 10^{-3}[/latex]	0.46	Germanium
[latex]-75 imes 10^{-3}[/latex]	640	Silicon
	[latex]10^{10} ext { to } 10^{14}[/latex]	Glass
	[latex]\sim 10^{13}[/latex]	Hard rubber
	[latex] 10^{15}[/latex]	Sulfur
	[latex]75 imes 10^{16}[/latex]	Quartz (fused)

Question 27.6: A resistance thermometer, which measures temperature by meas...

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