Linear expansion of thermometer column from reference point P

Steps:

• Expansion from 0°C to 100°C is 10.0 cm over 100°C change.
• Expansion is directly proportional to temperature change.
• At 50°C, temperature change is 50°C, or half of 100°C.
• Column length from P = (50/100) × 10.0 cm = 5.0 cm.

Why C is correct:

• Thermometer column height from the 0°C reference (P) increases linearly with temperature due to the liquid's coefficient of thermal expansion.

Why the others are wrong:

• A. 2.3 cm: Too low; equals ~23% of total expansion (23°C equivalent).
• B. 3.0 cm: Too low; equals 30% of total expansion (30°C equivalent).
• D. 7.0 cm: Adds irrelevant initial 2.0 cm to the 5.0 cm expansion.

Final answer: C