物理溫度計計數題目一問,急!!!!!!!20點!!!

The volumetric thermal expansion coefficient for mercury at room temperature is about 1.82 * 10^(-4) /C

3.6 cm = 36 mm
The volume of mercury = 0.01 mm^2 x 36 mm = 0.36 mm^2

You can calculate the new volume by this formula:
V(t) = V(1 + 1.82 x 10^(-4) x t + 7.8 x 10^(-9) x t^2),
where t is in °C, and V is the volume at 0°C

V(t) = V(1 + 1.82 x 10^(-4) t + 7.8 x 10^(-9)t^2)
V(100) = V(1 + 1.82 x 10^(-4) x 100 + 7.8 x 10^(-9) x (100)2)
V(100) = V(1 + 0.0182 + 0.000078)
V(100) = V(1.018278)
V(100) = 0.36 mm^2 (1.018278)
V(100) = 0.36658 mm^2

Alternatively, you can calculate by this way:
0.036 mm mm^2 + (0.36 mm^2 x coefficient of volumetric expansion x change in temperature)
The new volume at 100C = 0.36 mm^2 + [0.36 mm^2 x 1.82 * 10^(-4) x 100°]
The new volume at 100°C = 0.36 mm^2 + 0.006552 mm^2
The new volume at 100°C = 0.366552 mm^2

The height of mercury = volume/area of the tube
The height of mercury = (0.36658 mm^2)/(0.01 mm^2) = 36.65 mm

It is assume that expansion of glass tube is not taken into consideration. (coefficient of volume expansion for glass is 1.2x10^(-5)/C

The height of mercury = 36.65 mm at 100°C

The answer seems a bit funny. Please check carefully.

2010-09-16 05:24:55 補充：
To 發問者kam ying:

我翻譯答案成中文, 已經Email 給你. 請查看 Email. Good luck!

Godfrey

2010-09-16 05:31:20 補充：
CORRECTION:

In my solution, there is a careless mistake in the unit being used.
The unit of volume should be mm^3. (mm^2 is wrong)
I apologize for that.

Godfrey

3.007cm(2)