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?

at T = 0, R = 30

at T = 100, R = 40

if we assume linear behavior
T = m R + b

m = change in T/change in R = 100/40
= 2.5
so
T = 2.5 R + b
when T = 0, R = 30 so
0 = 2.5*30 + b
b = - 75
so
T = 2.5 R - 75
if R = 34.5 then
T = 2.5(34.5) - 75
T = 11.25 degrees C

To determine the temperature on a certain hot day using the given resistance values, we can use the concept of interpolation. This involves finding a value between two known points.

In this case, we have the resistance values at the ice point (30 ohms) and the steam point (40 ohms). The temperature at the ice point is 0 degrees Celsius, and the temperature at the steam point is 100 degrees Celsius.

First, we need to calculate the resistance difference between the steam point and the ice point:
Resistance difference = Resistance at steam point - Resistance at ice point = 40 ohms - 30 ohms = 10 ohms.

Next, we need to determine the resistance difference between the certain hot day and the ice point:
Resistance difference = Resistance at hot day - Resistance at ice point = 34.5 ohms - 30 ohms = 4.5 ohms.

We can then calculate the temperature difference between the steam point and the ice point:
Temperature difference = 100 degrees Celsius - 0 degrees Celsius = 100 degrees Celsius.

Now, we can calculate the temperature of the certain hot day using the equation:
Temperature at hot day = Temperature at ice point + (Resistance difference between hot day and ice point ÷ Resistance difference between steam point and ice point) × Temperature difference.

Substituting the values we obtained earlier:
Temperature at hot day = 0 degrees Celsius + (4.5 ohms ÷ 10 ohms) × 100 degrees Celsius.

Calculating further:
Temperature at hot day = 0 degrees Celsius + (0.45) × 100 degrees Celsius = 0 degrees Celsius + 45 degrees Celsius = 45 degrees Celsius.

Therefore, the temperature on the certain hot day is 45 degrees Celsius.