Question

When marking the fixed points on a thermometer its observed that at 0 degrees ,the mercury thread is of length 1 cm and 6 cm at 100degree .What temperature would correspond to the length of 4 cm

Answer 1

To find the temperature corresponding to a mercury thread length of 4 cm on the thermometer, we can use linear interpolation based on the lengths at the fixed points:

- At 0 degrees Celsius, the length is 1 cm.
- At 100 degrees Celsius, the length is 6 cm.

We can set up a linear relationship between the temperature (T) and the length (L) of the mercury thread.

1. Calculate the change in length per degree:
- Length change from 0°C to 100°C: \(6 \text{ cm} - 1 \text{ cm} = 5 \text{ cm}\)
- Temperature change: \(100 \text{°C} - 0 \text{°C} = 100 \text{°C}\)

Length per degree:
\[
\text{Length per degree} = \frac{5 \text{ cm}}{100 \text{°C}} = 0.05 \text{ cm/°C}
\]

2. Establish the equation for length:
\[
L = 1 + 0.05T
\]

3. Set \(L = 4\) cm and solve for \(T\):
\[
4 = 1 + 0.05T
\]
\[
4 - 1 = 0.05T
\]
\[
3 = 0.05T
\]
\[
T = \frac{3}{0.05} = 60 \text{°C}
\]

So, the temperature corresponding to a mercury thread length of 4 cm is **60 degrees Celsius**.