The question asks us to calculate the sensitivity of a platinum thermometer based on the provided table of resistance values at various temperatures. Understanding the sensitivity of an instrument is crucial for accurate measurement.

Sensitivity of Platinum Thermometer Measurement

The sensitivity of a measuring instrument, like a platinum thermometer, tells us how much the output changes for a given change in the input. In this context, the output is resistance (in Ohms, Ω) and the input is temperature (in degrees Celsius, °C). Therefore, the sensitivity will be expressed in Ω/°C.

The fundamental formula to calculate sensitivity (S) is:

\[S = \frac{\text{Change in Output}}{\text{Change in Input}}\]

For a platinum thermometer, this translates to:

\[S = \frac{\Delta \text{Resistance}}{\Delta \text{Temperature}} = \frac{\Delta R}{\Delta T}\]

Resistance and Temperature Data Analysis

Let's examine the provided data for the platinum thermometer, which lists corresponding resistance and temperature values:

To determine the sensitivity, we can select any two data points from this table. As observed from the table, the resistance increases consistently by 5 Ω for every 50 °C increase in temperature. This indicates a linear relationship, meaning the sensitivity should be constant across the given measurement range.

Calculating Instrument Sensitivity

Let's use the first two data points from the table to perform the calculation for the sensitivity of the measurement instrument:

• First data point: Resistance (\(R_1\)) = 200 Ω, Temperature (\(T_1\)) = 100 °C
• Second data point: Resistance (\(R_2\)) = 205 Ω, Temperature (\(T_2\)) = 150 °C

Next, we calculate the change in resistance ($\Delta R$) and the change in temperature ($\Delta T$):

• Change in Resistance ($\Delta R$) = \(R_2 - R_1 = 205\, \Omega - 200\, \Omega = 5\, \Omega\)
• Change in Temperature ($\Delta T$) = \(T_2 - T_1 = 150\, ^\circ\text{C} - 100\, ^\circ\text{C} = 50\, ^\circ\text{C}\)

Finally, we calculate the sensitivity (S) of the platinum thermometer instrument using the formula:

\[S = \frac{\Delta R}{\Delta T} = \frac{5\, \Omega}{50\, ^\circ\text{C}}\]

\[S = 0.1\, \Omega/^\circ\text{C}\]

This result implies that for every one degree Celsius change in temperature, the resistance of the platinum thermometer changes by 0.1 Ω. This consistent and predictable change is a key characteristic demonstrating the responsiveness and reliability of the instrument's measurement.