A mercury thread has 13cm and 24cm at the ice and steam point respectively, fine it temperature when the mercury thread is 19cm long.
ice-steam is 100°C
19 is 6/11 of the way from 13 to 24,
so the temperature is 6/11 * 100 = 54.54°C
To find the temperature when the mercury thread is 19cm long, we need to use the concept of linear expansion and the relationship between temperature and length.
First, let's define the initial length of the mercury thread at the ice point (L1) and the length at the steam point (L2). We are given that L1 = 13cm and L2 = 24cm.
We can use the formula for linear expansion:
ΔL = α * L * ΔT
where:
ΔL is the change in length,
α is the coefficient of linear expansion,
L is the original length, and
ΔT is the change in temperature.
We need to find the change in temperature (ΔT) when the mercury thread is 19cm long. Let's denote this length as L.
Since ΔL = L - L1 and ΔT = (ΔL / (α * L1)), we can rearrange the equation as:
ΔT = (L - L1) / (α * L1)
Now, substitute the given values into the equation:
ΔT = (19cm - 13cm) / (α * 13cm)
To find the temperature, we need the coefficient of linear expansion (α) for mercury.
The coefficient of linear expansion for mercury is α = 0.000181°C^(-1).
Now, let's calculate ΔT:
ΔT = (19cm - 13cm) / (0.000181 * 13cm)
ΔT = 6cm / (0.000181 * 13cm)
ΔT = 6 / 0.000181
ΔT ≈ 33198.34
Therefore, the change in temperature (ΔT) when the mercury thread is 19cm long is approximately 33198.34°C.
To find the temperature at 19cm, we add this change in temperature to the initial temperature at the ice point.
T = Ti + ΔT
where Ti is the initial temperature.
Since the ice point is defined as 0°C, Ti = 0°C.
T = 0°C + 33198.34°C
T ≈ 33198.34°C
Therefore, the temperature when the mercury thread is 19cm long is approximately 33198.34°C.