An ordinary mercury-in-glass thermometer is calibrated. In the ice water bath, the mercury level is 2.45 cm above the bulb. In boiling water at 1.00 atm pressure the mercury level is 17.75 cm above the bulb. What is the Celsius temperature when the level in 12.70 cm above the bulb?
---- = 17.75 = 100 C
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-------2.45 cm = 0 C
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O bulb
So zero is 2.45 cm above bulb and 100 C is 17.75 above the bulb; therefore, the 100 C mark is 15.3 cm (17.75-2.45) above the 0 C.
Where is the 12.70 cm? That is 12.70-2.45 - 10.25 cm above the zero mark. So the T should be
100 C x (10.25/15.3) = ?
To determine the Celsius temperature when the level is 12.70 cm above the bulb, we need to use the calibration points of the thermometer.
The first calibration point is in the ice water bath, where the mercury level is 2.45 cm above the bulb. This corresponds to the freezing point of water at 0 degrees Celsius.
The second calibration point is in boiling water at 1.00 atm pressure, where the mercury level is 17.75 cm above the bulb. This corresponds to the boiling point of water at 100 degrees Celsius.
Using this information, we can create a linear relationship between the height of the mercury level and the Celsius temperature.
First, let's calculate the total difference in mercury level between the boiling and freezing points:
17.75 cm - 2.45 cm = 15.30 cm
Next, we need to determine the distance of the desired point (12.70 cm) from the freezing point:
12.70 cm - 2.45 cm = 10.25 cm
Now, we can set up a proportion to find the Celsius temperature:
10.25 cm / 15.30 cm = x degrees Celsius / 100 degrees Celsius
Simplifying the proportion:
10.25 cm * 100 degrees Celsius = 15.30 cm * x degrees Celsius
1025 degrees Celsius = 15.30 cm * x degrees Celsius
Now, isolate x by dividing both sides of the equation by 15.30 cm:
1025 degrees Celsius / 15.30 cm = x degrees Celsius
x ≈ 66.99 degrees Celsius
Therefore, when the mercury level is 12.70 cm above the bulb, the Celsius temperature is approximately 66.99 degrees Celsius.