How far does the mercury rise in the capillary when the temperature changes from 0.0 C to 25.0 C?
The density of mercury at these temperatures is 13.596 g/cm^3 and 13.534 g/cm^3 , respectively.
Mercury is often used as an expansion medium in a thermometer. The mercury sits in a bulb on the bottom of the thermometer and rises up a thin capillary as the temperature rises. Suppose a mercury thermometer contains 3.350 grams of mercury and has a capillary that is 0.210 mm in diameter.
Express your answer with the appropriate units.
The first thing to do is to get the volume of Mercury for both temperatures. Then from the volume we can get the height of the mercury it has occupied at the temperature given using the formula for cylinder. Finally, we get the difference between the distances calculated.
`density = (mass)/(volume) = (g)/(cm^(3))`
`volume at speci fic temperature = (mass)/(density at speci fic temperature)`
`volume at 0^(o) C = (3.350 g Hg)/(13.596 (g Hg)/(cm^(3)))`
`volume at 0^(o)C = 0.2464 cm^(3)`
`volume at 25^(o)C = (3.350 gHg)/(13.534 (gHg)/(cm^(3)))`
`volume at 25^(o)C = 0.4275 cm^(3)`
The height of mercury for both temperatures:
`volume of cyli nder = volume of Hg = pi*r^(2)*h`
`h = (volume)/(pi*r^(2))`
where, `pi` = 3.1416; h = height and r = radius= diameter/2
radius = 0.210 mm/2 = 0.105mm = 0.0105cm
`h at 0^(o)C = (0.2464 cm^(3))/(3.1416*(0.0105cm)^2)`
`h at 0^(o)C = 711.386 cm`
`h at 25^(o) C = (0.2475cm^3)/(3.1416*(0.0105cm)^2)`
`h at 25^(o) C = 714.64 cm`
By subtracting the distances measured, we can have a value of 3.26 cm which is the final answer.