JAMB 2013 Physics · Question 14

Calculate the length which corresponds to a temperature of 20oC if the ice and steam points of an unguarded thermometer are 400 mm apart

Options

A.20mm
B.30mm
C.60mm
D.80mm

Answer: D. 80mm

Explanation written with AI and checked against the answer key

Analyze the question The thermometer's ice point (0°C) and steam point (100°C) are 400 mm apart on the stem. We need the length of mercury column above the ice point that corresponds to 20°C. (The word "unguarded" is likely "ungraduated" in the original question, meaning the thermometer has no scale marked.) Concept The length of the mercury thread changes uniformly with temperature, so: θ = (l_θ − l₀)/(l₁₀₀ − l₀) × 100 Here, l₁₀₀ − l₀ = 400 mm is the fundamental interval, and l_θ − l₀ is the length we want. Solution 20 = (l_θ − l₀)/400 × 100 l_θ − l₀ = (20 × 400)/100 = 80 mm Alternatively, 400 mm covers 100°C, so each degree is 4 mm, and 20°C × 4 mm/°C = 80 mm. Answer The length corresponding to 20°C is 80 mm, which is option D. Tip Find the length per degree first (fundamental interval ÷ 100), then multiply by the temperature. Here 400 ÷ 100 = 4 mm per °C, so 20°C gives 80 mm. This shortcut works for any thermometer-scale question.

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