In a thermometer manufacturing plant, a type of mercury thermometer is built at room temperature (20 °C) to measure temperatures in the 20 °C to 70 °C range, with a 1-cm3 spherical reservoir at the bottom and a 0.5-mm inner diameter expansion tube. The wall thickness of the reservoir and tube is negligible, and the 20 °C mark is at the junction between the spherical reservoir and the tube. The tubes and reservoirs are made of fused silica, a transparent glass form of SiO2 that has a very low linear expansion coefficient (α = 0.4∙10‒6 °C-1 ). By mistake, the material used for one batch of thermometers was quartz, a transparent crystalline form of SiO2 with a much higher linear expansion coefficient (α = 12.3 ∙ 10-6 °C-1 ). Will the manufacturer have to scrap the batch, or will the thermometers work fine, within the expected uncertainty of 5% in reading the temperature? The volume expansion coefficient of mercury is β = 181∙10-6 ° C- 1.
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