The resistances of a platinum resistance thermometer at the ice point, the steam point and the boiling point of sulphur are 2.50,3.50,and 6.50 respectively. find the boling point of sulphur on the platinum scale. the ice point and the steam point measure 0 and 100 respectively
To find the boiling point of sulfur on the platinum scale, we can make use of the concept of linear interpolation.
Linear interpolation allows us to estimate a value within a range of known values based on their relationship.
In this case, we have three known resistances for the ice point (0°C), steam point (100°C), and boiling point of sulfur. Let's label these resistances as R0, R100, and RB.
The first step is to determine the proportion of the resistance range between 0°C and 100°C that corresponds to the boiling point of sulfur. To do this, we calculate the ratio of the difference between the resistance of the boiling point and the ice point (RB - R0) to the difference between the steam point and the ice point (R100 - R0).
Ratio = (RB - R0) / (R100 - R0)
Next, we calculate the temperature range between 0°C and 100°C that corresponds to this ratio. The range is given by the product of the ratio and the temperature difference between the ice point and the steam point (100 - 0).
Temperature range = Ratio * (100 - 0)
Finally, we add the temperature range to the ice point temperature (0°C) to obtain the boiling point of sulfur on the platinum scale.
Boiling point of sulfur on the platinum scale = Temperature range + Ice point temperature
Now, let's plug in the values to calculate the boiling point of sulfur on the platinum scale:
Resistance at the ice point (R0) = 2.50
Resistance at the steam point (R100) = 3.50
Resistance at the boiling point of sulfur (RB) = 6.50
Ice point temperature = 0°C
Steam point temperature = 100°C
Ratio = (6.50 - 2.50) / (3.50 - 2.50) = 4 / 1 = 4
Temperature range = 4 * (100 - 0) = 400
Boiling point of sulfur on the platinum scale = 400 + 0 = 400°C
Therefore, the boiling point of sulfur on the platinum scale is 400°C.