The resistance of a platinum resistance thermometer is 30 ohms at ice point, 40 ohms at steam point, and 34.5 ohms are on certain holiday. What is the temperature of the day in Celsius temperature scale ?
Pls help me with this it is an assignment
the easy way is to graph it as a line.
the harder way is to solve the linear equations.
R=mT+b
30=m(273 )+b and
40=m(373)+b
subtracting equation 1 from 2
10=100m so m=.10
then solve for b.
then finally solve for Temp in R=mT+b remember T is in kelvins.
Thanks
To find the temperature of the day in Celsius using the given resistance values, we can use the concept of linear interpolation.
Linear interpolation is a method of estimating values within a range based on known data points. In this case, we can interpolate the temperature value corresponding to the given resistance of 34.5 ohms.
Here's how you can find the temperature:
Step 1: Calculate the resistance difference between the ice point and the steam point.
-> Resistance difference = Steam point resistance - Ice point resistance
-> Resistance difference = 40 ohms - 30 ohms = 10 ohms
Step 2: Calculate the resistance difference between the holiday resistance and the ice point resistance.
-> Resistance difference = Holiday resistance - Ice point resistance
-> Resistance difference = 34.5 ohms - 30 ohms = 4.5 ohms
Step 3: Calculate the temperature difference between the steam point and the ice point.
-> Temperature difference = Temperature at steam point - Temperature at ice point
-> Temperature difference = (100°C - 0°C) = 100°C
Step 4: Calculate the temperature difference based on the resistance difference.
-> Temperature difference = (Resistance difference / Resistance difference) * Temperature difference
-> Temperature difference = (4.5 ohms / 10 ohms) * 100°C
-> Temperature difference = 45°C
Step 5: Calculate the temperature at the holiday resistance.
-> Temperature at holiday = Temperature at ice point + Temperature difference at resistance
-> Temperature at holiday = 0°C + 45°C
-> Temperature at holiday = 45°C
Therefore, the temperature on the certain holiday is 45°C in the Celsius temperature scale.