The mercury manometer shown in FIGURE P16.50 so is attached...

The mercury manometer shown in FIGURE P16.50 so is attached to a gas cell. The mercury height $h$ is 120 mm when the cell is placed in an ice-water mixture. The mercury height drops to $30 \mathrm{mm}$ when the device is carried into an industrial freezer. What is the freezer temperature? Hint: The right tube of the manometer is much narrower than the left tube. What reasonable assumption can you make about the gas volume? (FIGURE CANNOT COPY)

The mercury manometer shown in FIGURE P16.50 so is attached to
a gas cell. The mercury height $h$ is 120 mm when the cell is placed in an ice-water mixture. The mercury height drops to $30 \mathrm{mm}$ when the device is carried into an industrial freezer. What is the freezer temperature? Hint: The right tube of the manometer is much narrower than the left tube. What reasonable assumption can you make about the gas volume?
(FIGURE CANNOT COPY)

Key Concepts

Temperature Conversion

In problems involving gases and pressure measurements, it is essential to convert temperature values into an absolute scale (Kelvin) when applying the ideal gas law. This ensures that the relationship between temperature and pressure is accurately maintained since the Kelvin scale directly correlates with the thermodynamic definition of temperature.

Manometer Operation

A manometer is an instrument used to measure pressure differences by balancing the weight of a column of liquid (usually mercury) against the pressure differential. In this scenario, the mercury height difference in the manometer indicates the pressure inside the gas cell. Since the manometer's design includes a much narrower tube on one side, it can be assumed that the gas's volume remains nearly fixed, focusing the change on pressure-induced height variations.

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, relates the pressure, volume, temperature, and amount of gas. In the context of a gas cell with a constant volume, any change in temperature directly affects the gas pressure. This principle is key in understanding how temperature changes in the gas cell result in observable changes in the mercury manometer reading.

Constant Volume Process

In a constant volume process, the volume of the gas does not change, so the pressure becomes directly proportional to the temperature. This relationship simplifies the analysis because any pressure variation measured by the manometer is solely a result of temperature fluctuations, allowing for a straightforward application of the ideal gas law.

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