a platinum resistance thermometer reads 0degrees and 100 degrees at ice point and boiling point of water respectively .the resistance of platinum wire varies with celcius temperature (theeta) as Rt=Ro(1+A(theeta)+B(theeta)square)

where A=3.8 into (10raised to the power-3)

B=5.6 into (10 raised to power-7)

what would be the reading of this thermometer if placed in a liquid bath at 50 degree celcius.?

please tell me the priciples to help me do this sum and if possible even the solution

thank you

To determine the resistance reading of a platinum resistance thermometer at 50 degrees Celsius, we can use the formula provided, which relates the resistance of the platinum wire to temperature. This formula is based on the principles of thermometry and the behavior of metals, particularly platinum, as they respond to temperature changes.

Understanding the Formula

The resistance of the platinum wire at a given temperature (Rt) is expressed as:

Rt = Ro(1 + Aθ + Bθ²)

In this equation:

• Rt is the resistance at temperature θ.
• Ro is the resistance at 0 degrees Celsius (ice point).
• A and B are temperature coefficients that account for the linear and quadratic variations of resistance with temperature.
• θ is the temperature in degrees Celsius.

Given Values

From your question, we have:

• A = 3.8 × 10^-3
• B = 5.6 × 10^-7
• θ = 50 degrees Celsius

Calculating the Resistance

To find the resistance at 50 degrees Celsius, we first need to know the value of Ro. Typically, for platinum thermometers, Ro is often taken as 100 ohms at 0 degrees Celsius. However, if you have a different value for Ro, you should use that instead.

Assuming Ro = 100 ohms, we can substitute the values into the formula:

Step-by-Step Calculation

1. Substitute the values into the formula:

Rt = 100(1 + (3.8 × 10^-3 × 50) + (5.6 × 10^-7 × 50²))

2. Calculate the linear term:

3.8 × 10^-3 × 50 = 0.19

3. Calculate the quadratic term:

5.6 × 10^-7 × 50² = 5.6 × 10^-7 × 2500 = 1.4 × 10^-3

4. Add these results to find the total factor:

1 + 0.19 + 0.0014 = 1.1914

5. Finally, calculate Rt:

Rt = 100 × 1.1914 = 119.14 ohms

Final Result

Therefore, the reading of the platinum resistance thermometer when placed in a liquid bath at 50 degrees Celsius would be approximately 119.14 ohms.

This calculation illustrates how the resistance of platinum varies with temperature, allowing us to accurately measure temperature in various applications. If you have any further questions about this process or related concepts, feel free to ask!