To determine the temperature at which the resistance of the wire is 0.90 ohm, we can use the formula for the resistance-temperature relationship of a material. This formula is:
R = R0 * (1 + α * (T - T0))
Where:
R is the resistance at temperature T
R0 is the resistance at a reference temperature T0
α is the temperature coefficient of resistance for the material
In this case, we have two data points:
R1 = 0.75 ohm at T1 (ice point)
R2 = 1.05 ohm at T2 (steam point)
We can use these points to determine the temperature coefficient of resistance (α) for platinum.
We can rearrange the formula to solve for α:
α = (R2 - R1) / (R1 * (T2 - T1))
Plugging in the values, we have:
α = (1.05 - 0.75) / (0.75 * (100 - 0)) = 0.4 / 75 = 0.0053 /°C
Now we can use this value of α to find the temperature (T) at which the resistance is 0.90 ohm:
0.90 = 0.75 * (1 + 0.0053 * (T - 0))
0.90 / 0.75 = 1 + 0.0053T
0.90 / 0.75 - 1 = 0.0053T
(0.90 - 0.75) / 0.75 = 0.0053T
0.15 / 0.75 = 0.0053T
0.20 = 0.0053T
T = 0.20 / 0.0053
T ≈ 37.74 °C
Therefore, the temperature at which the resistance of the wire is 0.90 ohm is approximately 37.74°C.
However, none of the given answer options match this value exactly.
The resistance of a platinum
wire at the ice and steam points
are 0.75 ohm and 1.05 ohm
respectively. Determine the
temperature at which the
resistance of the wire is 0.90
ohm?
A. 43.0 °C
B. 50.0°C
C. 69.9°C
D. 87.0°C
1 answer