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2. In an alcohol-in-glass thermometer, the alcohol column has length `11.82\ cm` at `0.0°C` and length `22.85\ cm` at `100.0°C`. What is the temperature if the column has length (a) `16.70\ cm` and (b) `20.50\ cm`
2. In an alcohol-in-glass thermometer, the alcohol column has length 11.82\ cm at 0.0°C and length 22.85\ cm at 100.0°C. What is the temperature if the column has length (a) 16.70\ cm and (b) 20.50\ cm (a)`T = 44.2°C`
(b)`T = 78.7C`
Given:
`L_(0°C) = 11.82\ cm`
`L_(100°C) = 22.85\ cm`
Solution:
First we need find out the change in temperature per unit length change.
`(∆T)/(∆L) = (100.0°C - 0.0°C)/(22.85\ cm -11.82\ cm) = 9.066 C°//cm`
`T = 0.0°C + (L-L_(0°C))(∆T)/(∆L)`
(a)
When `L = 16.7\ cm`
`T = 0.0°C + (16.70\ cm -11.82\ cm)(9.066 C°//cm)`
`T = 44.2°C`
(b)
When `L = 78.7\ cm`
`T = 0.0°C + (20.50\ cm -11.82\ cm)(9.066 C°//cm)`
`T = 78.7C` |