The lower and upper fixed points marked on a Mercury-in-glass thermometer are 210mm apart. The end of the…

Analysis

To solve this problem, we need to relate the physical length of the mercury column to the temperature scale. In a standard Celsius thermometer, the lower fixed point (ice point) is $0^\circ\text{C}$ and the upper fixed point (steam point) is $100^\circ\text{C}$.

Concept

The temperature on a linear scale can be calculated using the ratio of the length of the mercury column above the lower fixed point to the total length between the fixed points:

Where:

• $L_t$ = Length of the mercury column at the room temperature
• $L_0$ = Length at the lower fixed point ($0^\circ\text{C}$)
• $L_{100}$ = Length at the upper fixed point ($100^\circ\text{C}$)
• $(L_{100} - L_0)$ = The total distance between fixed points (given as $210\text{mm}$)
• $(L_t - L_0)$ = The distance of the mercury column above the lower fixed point (given as $49\text{mm}$)

Solution

1. Identify the given values: • Total distance ($L_{100} - L_0$) = $210\text{mm}$ • Distance above lower fixed point ($L_t - L_0$) = $49\text{mm}$

2. Apply the formula: $$\text{Temperature} = \left( \frac{49}{210} \right) \times 100^\circ\text{C}$$

3. Perform the calculation: $$\text{Temperature} = \frac{4900}{210}$$ $$\text{Temperature} = \frac{490}{21}$$ $$\text{Temperature} \approx 23.33^\circ\text{C}$$

Conclusion

Comparing our result to the given options, $23.3^\circ\text{C}$ matches option B.

Exam Tip

When dealing with thermometer problems, always remember that the ratio of the "part" to the "whole" remains constant regardless of the units used (mm, cm, or inches). Just ensure you are consistent with your measurements!