- #1
a077456
- 6
- 0
A typical mercury thermometer is made up of a thin, cylindrical capillary tube with a diameter of 0.0040 cm, and the spherical bulb with a diameter of 0.25 cm. If we DON'T Neglect the expansion of the glasas, find the change in height of the mercury column for a temperature change of 30 degree.
In the solution, it was given that the thermal volume expansion of mercury = 18 * 10-5 and the thermal volume expansion of glass = 2 x 10-5
I have attempted to solve the problem, however, I don't really know which volume expansion value should I use in the problem.
I have setup:
[tex]\Delta[/tex] V = Vexpansion
(V0 + [tex]\Delta[/tex]A) * [tex]\Delta[/tex]h = V0 + V0 * volume expansion value * [tex]\Delta[/tex] Temperature
[tex]\Pi[/tex] *(0.0040 cm/2)2 + [tex]\Pi[/tex] *(0.0040 cm/2)2 * ( thermal expansion of "what material?" * (30 degree) * ([tex]\Delta[/tex] h =( ([tex]\frac{4}{3}[/tex] * [tex]\Pi[/tex] * (0.25cm/2)3 ) + ([tex]\frac{4}{3}[/tex] * [tex]\Pi[/tex] * (0.25cm/2)3 * (volume expansion of "which material" ) * (30 degree)
I have tried to solve with both thermal expansion number, however, I have got 650 cm and 631cm.
The solution of the problem is [tex]\Delta[/tex] h = 3.1cm...
I wonder where did I do wrong? Whcih volume of expansion should I choose?
In the solution, it was given that the thermal volume expansion of mercury = 18 * 10-5 and the thermal volume expansion of glass = 2 x 10-5
The Attempt at a Solution
I have attempted to solve the problem, however, I don't really know which volume expansion value should I use in the problem.
I have setup:
[tex]\Delta[/tex] V = Vexpansion
(V0 + [tex]\Delta[/tex]A) * [tex]\Delta[/tex]h = V0 + V0 * volume expansion value * [tex]\Delta[/tex] Temperature
[tex]\Pi[/tex] *(0.0040 cm/2)2 + [tex]\Pi[/tex] *(0.0040 cm/2)2 * ( thermal expansion of "what material?" * (30 degree) * ([tex]\Delta[/tex] h =( ([tex]\frac{4}{3}[/tex] * [tex]\Pi[/tex] * (0.25cm/2)3 ) + ([tex]\frac{4}{3}[/tex] * [tex]\Pi[/tex] * (0.25cm/2)3 * (volume expansion of "which material" ) * (30 degree)
I have tried to solve with both thermal expansion number, however, I have got 650 cm and 631cm.
The solution of the problem is [tex]\Delta[/tex] h = 3.1cm...
I wonder where did I do wrong? Whcih volume of expansion should I choose?