A resistance thermometer is a thermometer in which the electrical resistance changes with temperature. We are free to define temperatures measured by such a thermometer in kelvins (K) to be directly proportional to the resistance R, measured in ohms (Ω). A certain resistance thermometer is found to have a resistance R of 90.35 Ω When its bulb is placed in water at triple-point temperature (273.16 K). what temperature is indicated by the thermometer if the bulb is placed in an environment such that its resistance is 96.28 Ω?

To determine the temperature indicated by the resistance thermometer when its resistance is 96.28 Ω, we can use the relationship between resistance and temperature. Since we know that the resistance is directly proportional to the temperature in kelvins, we can set up a simple ratio based on the known values.

Understanding the Relationship

In this case, we have two key points:

• The resistance at the triple-point temperature (273.16 K) is 90.35 Ω.
• The resistance we want to analyze is 96.28 Ω.

Setting Up the Proportionality

Since the resistance is directly proportional to the temperature, we can express this relationship mathematically as:

R1 / T1 = R2 / T2

Where:

• R1 = 90.35 Ω (resistance at 273.16 K)
• T1 = 273.16 K (temperature at R1)
• R2 = 96.28 Ω (resistance we want to find the temperature for)
• T2 = ? (temperature corresponding to R2)

Calculating the Temperature

We can rearrange the equation to solve for T2:

T2 = (R2 * T1) / R1

Now, substituting the known values:

T2 = (96.28 Ω * 273.16 K) / 90.35 Ω

Performing the Calculation

Now, let's do the math step-by-step:

• First, calculate the numerator: 96.28 * 273.16 = 26244.0768
• Next, divide by the resistance at the triple-point: 26244.0768 / 90.35 ≈ 290.38 K

Final Result

The temperature indicated by the thermometer when its resistance is 96.28 Ω is approximately 290.38 K.

Summary

This example illustrates how resistance thermometers work based on the principle of direct proportionality between resistance and temperature. By using known values and a simple ratio, we can easily find the temperature corresponding to any given resistance.