A mercury thermometer has a bulb of volume 0.100 cm

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. A mercury thermometer has a glass bulb of interior

volume 0.100 cm3 at 10°C. The glass capillary tubeabove the bulb has an inner cross-sectional area of0.012 mm². The coefficient of volume expansion ofmercury is 1.8 * 10 4 K-1. If the expansion of theglass is negligible, how much will the mercury risein the capillary tube when the temperature rises from5°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​

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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.


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