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Explain the working of a clinical thermometer, including the choice of liquid, reasons for not using water, the purpose of the narrow bore, and how to calculate body temperature from observed length.

Physics

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Answer

b

40∘C\text{}40^\circ\text{C}

Step-by-step solution

4 steps

Here's the breakdown of "Item two":

Part a(i)

The device the doctor used is a thermometer, specifically a *clinical thermometer

Part a(ii)

The liquids that can be used to make a thermometer are mercury and *alcohol

Part a(iii)

Explanation to the mother

  • Why water is not used to make the device? Water is not suitable because it has a high specific heat capacity (meaning it takes a lot of heat to change its temperature), it expands anomalously (it contracts from 0∘C0^\circ\text{C} to 4∘C4^\circ\text{C} before expanding), it wets glass, and its freezing point (0∘C0^\circ\text{C}) and boiling point (100∘C100^\circ\text{C}) limit its useful temperature range for many applications, including body temperature measurement.
  • Why device had narrow bore? A narrow bore (capillary tube) makes the thermometer more sensitive. A small change in the liquid's volume due to temperature change causes a significant and easily observable change in the length of the liquid column, allowing for precise readings.

Part b

40∘C\text{}40^\circ\text{C}

To find the child's body temperature, we use the principle of linear expansion for a thermometer.

  1. Identify the known values.

    The length of the liquid column from the lower fixed point is 6.6 cm6.6\,\text{cm}.
    The total length between the lower fixed point (0∘C0^\circ\text{C}) and the upper fixed point (100∘C100^\circ\text{C}) is 16.5 cm16.5\,\text{cm}.

  2. Use the formula for temperature on a linear scale.

    The temperature θ\theta can be calculated using the formula:

    θ=Length of liquid column from lower fixed pointLength between upper and lower fixed points×(Upper fixed point−Lower fixed point)+Lower fixed point\theta = \frac{\text{Length of liquid column from lower fixed point}}{\text{Length between upper and lower fixed points}} \times (\text{Upper fixed point} - \text{Lower fixed point}) + \text{Lower fixed point}

    For the Celsius scale, the lower fixed point is 0∘C0^\circ\text{C} and the upper fixed point is 100∘C100^\circ\text{C}.

  3. Substitute the values into the formula.

    θ=6.6 cm16.5 cm×(100∘C−0∘C)+0∘C\theta = \frac{6.6\,\text{cm}}{16.5\,\text{cm}} \times (100^\circ\text{C} - 0^\circ\text{C}) + 0^\circ\text{C}

  4. Calculate the temperature.

    θ=6.616.5×100∘C\theta = \frac{6.6}{16.5} \times 100^\circ\text{C} θ=0.4×100∘C\theta = 0.4 \times 100^\circ\text{C} θ=40∘C\theta = 40^\circ\text{C}

    The child's body temperature is 40∘C\boxed{\text{}40^\circ\text{C}}.

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