The resistance of platinum thermometer is 11ohm when dipped in a triple point cell.when dipped in a bath the resistance is 28.887ohm.Find the temperature of the bath in °c on a platinum scale.

To determine the temperature of the bath using the resistance values of the platinum thermometer, we can apply the principles of the resistance-temperature relationship for platinum. Platinum thermometers operate on the principle that the resistance of platinum changes with temperature in a predictable manner. The relationship can often be expressed using the Callendar-Van Dusen equation, but for simplicity, we can use a linear approximation for small temperature ranges.

Understanding the Basics

The resistance of a platinum thermometer at the triple point of water (0 °C) is known to be a specific value. In your case, the resistance is 11 ohms at the triple point. When the thermometer is placed in a bath, the resistance increases to 28.887 ohms. The change in resistance can be used to calculate the temperature of the bath.

Linear Resistance-Temperature Relationship

The relationship between temperature and resistance for platinum can be approximated as:

• R(T) = R0(1 + αT)

Where:

• R(T) is the resistance at temperature T.
• R0 is the resistance at 0 °C (11 ohms in this case).
• α is the temperature coefficient of resistance for platinum, approximately 0.00385 °C^-1 for a standard platinum thermometer.
• T is the temperature in degrees Celsius.

Calculating the Temperature

We can rearrange the formula to solve for T:

• T = (R(T)/R0 - 1) / α

Substituting the known values:

• R(T) = 28.887 ohms
• R0 = 11 ohms
• α = 0.00385 °C^-1

Now, plug in the values:

• T = (28.887 / 11 - 1) / 0.00385

Calculating the fraction:

• 28.887 / 11 = 2.6261
• 2.6261 - 1 = 1.6261

Now, divide by α:

• T = 1.6261 / 0.00385 ≈ 422.5 °C

Final Result

The temperature of the bath, based on the resistance readings of the platinum thermometer, is approximately 422.5 °C.

This calculation illustrates how the resistance of a platinum thermometer can be used to accurately measure temperature, leveraging the predictable change in resistance with temperature. If you have any further questions or need clarification on any of the steps, feel free to ask!