Calculate the temperature of a hot liquid using an uncalibrated thermometer given the lengths of the mercury thread at 0°C, 100°C, and in the liquid.

Step 1: Identify the known values and the formula for an uncalibrated thermometer.
The length of the mercury thread at $0^\circ\text{C}$ (melting ice) is $L_0 = 18 \text{ mm}$.
The length of the mercury thread at $100^\circ\text{C}$ (steam) is $L_{100} = 138 \text{ mm}$.
The length of the mercury thread in the hot liquid is $L_T = 118 \text{ mm}$.

The temperature $T$ on a linear scale can be found using the formula:

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