Question

When making the fixed points on a thermometer, it is observed that at 0 degrees Celsius the mercury thread is of length 2cm and 8cm at 100 degrees Celsius. What temperature would correspond to a length of 6 cm

Answer 1

To find the temperature corresponding to a length of 6 cm on the thermometer, we can use linear interpolation between the known points:

1. At 0 degrees Celsius, the length is 2 cm.
2. At 100 degrees Celsius, the length is 8 cm.

Let's denote the length \( L \) in cm as follows:
- \( L_0 = 2 \) cm at \( T_0 = 0 \) degrees Celsius
- \( L_{100} = 8 \) cm at \( T_{100} = 100 \) degrees Celsius

Now, we can use the formula for linear interpolation:

\[
T = T_0 + \frac{(L - L_0)(T_{100} - T_0)}{(L_{100} - L_0)}
\]

Substituting the known values:

- Length \( L = 6 \) cm
- \( T_0 = 0 \)
- \( T_{100} = 100 \)
- \( L_0 = 2 \) cm
- \( L_{100} = 8 \) cm

Now we will calculate:

\[
T = 0 + \frac{(6 - 2)(100 - 0)}{(8 - 2)}
\]
\[
T = 0 + \frac{(4)(100)}{6}
\]
\[
T = \frac{400}{6} = \frac{200}{3} \approx 66.67 \text{ degrees Celsius}
\]

Thus, a length of 6 cm corresponds to approximately **66.67 degrees Celsius**.