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A liquid column in a liquid-in-glass thermometer is 2.0 cm long at 0 °C. The column expands by 10.0 cm when heated to 100 °C.*1 pointMeasuring from P, how long is the liquid column at 30 °C?

Question

A liquid column in a liquid-in-glass thermometer is 2.0 cm long at 0 °C. The column expands by 10.0 cm when heated to 100 °C.*1 pointMeasuring from P, how long is the liquid column at 30 °C?

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Solution

To solve this problem, we first need to understand that the expansion of the liquid in the thermometer is linear with temperature. This means that for every degree Celsius increase in temperature, the liquid column expands by a certain fixed amount.

From the problem, we know that the liquid column expands by 10.0 cm when heated from 0 °C to 100 °C. This is a temperature change of 100 °C. Therefore, the expansion per degree Celsius is 10.0 cm / 100 °C = 0.1 cm/°C.

Now, we want to find the length of the liquid column at 30 °C. This is a temperature increase of 30 °C from 0 °C. Therefore, the expansion of the liquid column is 0.1 cm/°C * 30 °C = 3.0 cm.

Since the liquid column was initially 2.0 cm long at 0 °C, the length of the liquid column at 30 °C is 2.0 cm + 3.0 cm = 5.0 cm.

This problem has been solved

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