Final answer:
The resistance of a platinum wire temperature sensor at a temperature of 250 K can be calculated using a proportionality relation between resistance and temperature. The resistance is directly proportional to temperature, so we can set up a proportion to find the resistance at 250 K. By solving the proportion, we find that the resistance is approximately 8062.5 ohms.
Step-by-step explanation:
The resistance of a platinum wire temperature sensor at a temperature of 250 K can be found using the proportionality relation between resistance and temperature. Since the sensor is directly proportional to temperature, we can set up a proportion with known values:
R1 / T1 = R2 / T2
Substituting the given values, we have:
R1 / 250 K = R2 / 20 K
Cross-multiplying and solving for R2:
R2 = (R1 / T1) * T2
Given R1 = 645 ohms and T1 = 20 K, we can calculate:
R2 = (645 ohms / 20 K) * 250 K = 8062.5 ohms
Therefore, the resistance of the platinum wire temperature sensor at a temperature of 250 K is approximately 8062.5 ohms.