The resistance of a platinum resistance thermometer is 30 ohms at the ice point, 40 ohms at the steam point and 34.5 ohms on a certain hot day, what is the temperature of the day on celcius temperature day?
been there, done that
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Answer the question
To find the temperature on a certain day, we can use a linear interpolation formula based on the resistance values at known temperatures.
Given:
Resistance at the ice point (0°C) = 30 ohms
Resistance at the steam point (100°C) = 40 ohms
Resistance on the certain hot day = 34.5 ohms
Step 1: Determine the resistance range
The resistance range is the difference between the resistance at the steam point and the resistance at the ice point:
Resistance range = 40 ohms - 30 ohms = 10 ohms
Step 2: Calculate the ratio of the measured resistance within the range
The measured resistance falls within the resistance range, so we can find the ratio using the following formula:
Ratio = (Measured Resistance - Resistance at the Ice point) / Resistance range
Ratio = (34.5 ohms - 30 ohms) / 10 ohms
Ratio = 4.5 ohms / 10 ohms
Ratio = 0.45
Step 3: Calculate the temperature using the ratio
The temperature can be calculated using the following formula:
Temperature = Temperature at the Ice point + (Ratio * Temperature range)
Temperature = 0°C + (0.45 * 100°C)
Temperature = 0°C + 45°C
Temperature = 45°C
Therefore, the temperature on the certain hot day is 45 degrees Celsius.