The tube of a mercury thermometer has an inside diameter of 0.130 mm. The bulb has a volume of 0.270 cm^3.
How far will the thread of mercury move when the temperature changes from 13.5 ∘C to 32.5 ∘C? Take into account expansion of the Pyrex glass.
To determine how far the thread of mercury will move, we need to consider the expansion of both the mercury and the Pyrex glass.
The expansion of the mercury can be calculated using the coefficient of volume expansion (β) for mercury. The equation for the change in volume (ΔV) of a substance due to a change in temperature (ΔT) is:
ΔV = β * V * ΔT
Where:
- β is the coefficient of volume expansion
- V is the initial volume of the substance
- ΔT is the change in temperature
For mercury, the coefficient of volume expansion (β) is approximately 1.82 x 10^-4 per degree Celsius.
First, we need to calculate the change in volume of the mercury. Since the volume of the bulb is given as 0.270 cm^3, we can consider this as the initial volume (V) of the mercury.
ΔV = (1.82 x 10^-4 per °C) * (0.270 cm^3) * (32.5 - 13.5) °C
Now, let's calculate the change in volume:
ΔV = (1.82 x 10^-4 per °C) * (0.270 cm^3) * (19 °C)
Next, we need to calculate the change in length of the thread of mercury. The change in volume of the mercury will cause a corresponding change in the length of the thread.
The change in length (ΔL) can be calculated using the equation:
ΔL = ΔV / A
Where:
- ΔL is the change in length
- ΔV is the change in volume of the mercury
- A is the cross-sectional area of the tube
To find the cross-sectional area of the tube, we need to calculate the radius first. The inside diameter of the tube is given as 0.130 mm, so the radius (r) can be calculated by dividing the diameter by 2:
r = 0.130 mm / 2 = 0.065 mm = 0.065 x 10^-3 cm
Now, we can calculate the cross-sectional area (A) of the tube:
A = π * r^2
Let's calculate the cross-sectional area:
A = 3.14 * (0.065 x 10^-3 cm)^2
Now, we can calculate the change in length:
ΔL = ΔV / A
Finally, you can plug in the calculated values to find the change in length of the thread of mercury when the temperature changes from 13.5 °C to 32.5 °C.