The lenght of the mercury column of a mercury thermometer are 1.08cm and 20.98cm respectively at the standard fixed points. What is the temperature of the body which produces 8.0cm of this mercury column?
The standard fixed points are to be the freezing point and boiling point of water, namely 0 and 100°Celsius.
By proportions,
temperature = (8-1.08)/(20.98-1.08)*100
=34.8°C
In case of Fahrenheit,
temperature = (8-1.08)/(20.98-1.08)*180+32
=94.6°F
To find the temperature of the body that produces 8.0 cm of the mercury column, we can use the concept of linear expansion.
First, we need to calculate the expansion coefficient of mercury (α). The expansion coefficient represents how much a substance expands or contracts with changes in temperature.
Next, we can use the formula for linear expansion:
ΔL = L0 * α * ΔT
Where:
ΔL is the change in length
L0 is the original length
α is the expansion coefficient
ΔT is the change in temperature
We can rearrange the formula to solve for ΔT:
ΔT = ΔL / (L0 * α)
Given that the original length (L0) is 20.98 cm and the change in length (ΔL) is 8.0 cm, we need to find the expansion coefficient (α) to calculate the change in temperature (ΔT).
Unfortunately, the value of α for mercury is not provided. However, as a general rule, the expansion coefficient for mercury is approximately 0.000181 per degree Celsius.
Using this approximate value, we can calculate ΔT:
ΔT = 8.0 cm / (20.98 cm * 0.000181)
Calculating the above expression gives us ΔT ≈ 24.97 °C.
Therefore, the temperature of the body that produces 8.0 cm of the mercury column is approximately 24.97 °C.