(PLEASE HELP ME URGENTLY) The electrical resistances of the element in a platinum resistance thermometer at 100°C, 0°C and room temperature are 75.000W, 63.000W and 64.992W respectively. Use these data to determine the room temperature. (PLEASE HELP ME OUT URGENTLY)😓😓

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Resistances are not in Watts but in Ohms.

assume linear
R = m T + b
75 = 100 m + b
64 = 0 m + b
so
b = 64
75 = 100 m + 64
m = 0.11
so
R = .11 T + 64
now put in 64.992 for R and solve for T

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To determine the room temperature using the given data, we can use the relationship between resistance and temperature for a platinum resistance thermometer. This relationship is typically described by the Callendar-Van Dusen equation:

Rt = R0 * (1 + A * t + B * t^2)

Where:
Rt is the resistance at a given temperature t
R0 is the resistance at 0°C (given as 63.000Ω in this case)
A and B are coefficients that depend on the characteristics of the platinum element

Since we have the resistances at three different temperatures, we can set up three equations using the Callendar-Van Dusen equation for 100°C, 0°C, and room temperature, and solve them simultaneously to find the value of the room temperature.

Let's use the given resistance values:

R100 = 75.000Ω
R0 = 63.000Ω
Rroom = 64.992Ω

Using the Callendar-Van Dusen equation, we can write the following equations:

R100 = R0 * (1 + A * 100 + B * 100^2)
R0 = R0 * (1 + A * 0 + B * 0^2)
Rroom = R0 * (1 + A * Tr + B * Tr^2)

Now we need to solve these three equations simultaneously to find the value of Tr (room temperature).

Simplifying the equations:

75.000 = 63.000 * (1 + 100A + 10000B) -- Equation 1
63.000 = 63.000 * (1 + 0A + 0B) -- Equation 2
64.992 = 63.000 * (1 + TrA + Tr^2B) -- Equation 3

Dividing Equation 1 and Equation 2 by 63.000:

75.000/63.000 = 1 + 100A + 10000B -- Equation 4
1 = 1 + 0A + 0B -- Equation 5

Simplifying Equation 5:

0 = 100A + 10000B -- Equation 6

Substituting Equation 6 into Equation 4:

75.000/63.000 = 1 + 0 -- Equation 7
75.000/63.000 = 1

Now we have a single equation:

75.000/63.000 = 1

Simplifying this equation:

1.1904761904761904761904761904762 = 1

Since this equation is not possible, it appears there may be an error or inconsistency in the given data. Please double-check the values and coefficients provided.