. A mercury thermometer has a glass bulb of interior
volume 0.100 cm3 at 10°C. The glass capillary tube
above the bulb has an inner cross-sectional area of
0.012 mm². The coefficient of volume expansion of
mercury is 1.8 * 10 4 K-1. If the expansion of the
glass is negligible, how much will the mercury rise
in the capillary tube when the temperature rises from
5°C to 35°C if the bulb was full at 5°C?
(a) 0.45 mm
(6) 4.5 mm
(c) 45 mm
(d) 45 cm
Answers
Answer:
A mercury thermometer has a bulb of volume 0.100 cm3 at 10oC. The capillary tube above the bulb has a cross-sectional area of 0.012 mm2. The volume thermal expansion coefficient of mercury is 1.8*10-4 (oC)-1. How much will the mercury rise when the temperature rises by 20oC?
Solution:
Concepts:
The volume expansion coefficient
The average volume expansion coefficient b is defined through ΔV = βVΔT.
Reasoning:
The volume of the mercury will increase as the temperature rises and the mercury will rise in the capillary tube.
Details of the calculation:
The increase in temperature is 20oC. The change in the volume of the mercury is
ΔV = βVΔT = (1.8*10-4 (oC)-1)(0.100 cm3)(20 oC) = 3.6*10-4 cm3 = 0.36 mm3.
Δh = ΔV/A = (0.36 mm3)/(0.012 mm2) = 30 mm.
The mercury will rise 30 mm.