Answer:
[tex]34.2^{\circ}C[/tex]
Explanation:
The resistance increases linearly with the temperature - so we can write:
[tex]\Delta R = k \Delta T[/tex]
where
[tex]\Delta R[/tex] is the change in resistance
k is the coefficient of proportionality
[tex]\Delta T[/tex] is the variation of temperature
In the first part of the problem, we have
[tex]\Delta R = 17.35 - 11.50 =5.85\Omega[/tex]
[tex]\Delta T = 100 -0 = 100^{\circ}C[/tex]
So the coefficient of proportionality is
[tex]k=\frac{\Delta R}{\Delta T}=\frac{5.85}{100}=0.0585 \Omega ^{\circ}C^{-1}[/tex]
When the resistance is [tex]R=13.50\Omega[/tex], the change in resistance with respect to the resistance at zero degrees is
[tex]\Delta R' = 13.50-11.50 = 2.00 \Omega[/tex]
So we can find the change in temperature as:
[tex]\Delta T' = \frac{\Delta R}{k}=\frac{2.00}{0.0585}=34.2^{\circ}[/tex]
So the new temperature is
[tex]T_f = T_0 + \Delta T' = 0+34.2 = 34.2^{\circ}C[/tex]
