NECO 2001 Physics · Question 35

The lower and upper fixed points of a mercury-in-glass thermometer are marked X and 180 mm respectively. On a…

Question

The lower and upper fixed points of a mercury-in-glass thermometer are marked X and 180 mm respectively. On a particular day the mercury meniscus in the thermometer rises to 60mm. If the corresponding reading on a Celsius scale is 20 ° C, what is the value X?

A.6.0mm
B.18.0mm
C.30.0mm
D.60.0mm
E.120.0mm

Answer: C. 30.0mm

Explanation written with AI and checked against the answer key

Analyze the question: The thermometer has a lower fixed point (ice point, 0°C) at X mm and an upper fixed point (steam point, 100°C) at 180 mm. The mercury is at 60 mm when the temperature is 20°C. We need X. Concept: For a linear thermometer, the temperature is proportional to the length of the mercury thread above the lower fixed point: θ = (L_θ − L₀)/(L₁₀₀ − L₀) × 100 Solution: 20 = (60 − X)/(180 − X) × 100 20/100 = (60 − X)/(180 − X) 1/5 = (60 − X)/(180 − X) 180 − X = 5(60 − X) 180 − X = 300 − 5X 4X = 120 X = 30 mm Check: The range is 180 − 30 = 150 mm. The mercury is 60 − 30 = 30 mm above the lower point, and 30/150 = 0.2, which is 20% of 100°C = 20°C. ✓ Answer: C. 30.0 mm Tip: For thermometer problems, use the ratio (reading − lower point)/(upper point − lower point) = θ/100. Always check by substituting your answer back in.

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