To determine the reading on the millimeter scale of an ungraduated mercury thermometer at a temperature of 20°C, we can use the information given for the readings in ice and steam to interpolate the value.
First, we need to determine the length of the mercury column for the given temperatures of ice and steam. Let's call the length in ice L_ice and the length in steam L_steam.
Given:
- Length in ice (L_ice) = 22.8 mm
- Length in steam (L_steam) = 243 mm
Next, we need to determine the temperature coefficient of the thermometer. This coefficient represents the change in length per degree Celsius (mm/°C) for the specific thermometer.
Since the thermometer is ungraduated, we'll assume it has a linear expansion coefficient similar to a standard mercury thermometer. The average coefficient of linear expansion for mercury is approximately 0.18 mm/°C.
Now, we can calculate the length of the mercury column at 20°C (L_20) using linear interpolation:
L_20 = L_ice + (L_steam - L_ice) * (T_20 - T_ice) / (T_steam - T_ice)
Substituting the known values: L_20 = 22.8 mm + (243 mm - 22.8 mm) * (20°C - 0°C) / (100°C - 0°C)
Simplifying the equation: L_20 = 22.8 mm + (243 mm - 22.8 mm) * 20 / 100
Calculating: L_20 = 22.8 mm + (220.2 mm) * 20 / 100 L_20 = 22.8 mm + 44.04 mm L_20 = 66.84 mm
Therefore, the millimeter reading on the thermometer at a temperature of 20°C would be approximately 66.84 mm.