A weather balloon is inflated to a volume of 28.5 L at a pressure of 748 mm Hg and a temperature

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A weather balloon is inflated to a volume of 28.5 L at a...

A weather balloon is inflated to a volume of 28.5 $\mathrm{L}$ at a pressure of 748 $\mathrm{mm} \mathrm{Hg}$ and a temperature of $28.0^{\circ} \mathrm{C}$ The balloon rises in the atmosphere to an altitude of approximately $25,000 \mathrm{ft},$ where the pressure is 385 $\mathrm{mm} \mathrm{Hg}$ and the temperature is $-15.0^{\circ} \mathrm{C}$ . Assuming the balloon can freely expand, calculate the volume of the balloon at this altitude.

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Key Concepts

Combined Gas Law

The combined gas law relates the pressure, volume, and temperature of a given amount of gas. It states that for a fixed amount of gas, the ratio of the product of pressure and volume to temperature remains constant (P?V?/T? = P?V?/T?). This law is crucial for solving problems where a gas undergoes changes in pressure, volume, and temperature simultaneously.

Temperature Conversion

Temperature must be expressed in an absolute scale, such as Kelvin, when using gas laws. Converting from Celsius to Kelvin is essential because the gas laws are based on absolute temperature, ensuring correct proportional relationships between variables.

Pressure-Volume Relationship

This concept describes how the volume of a gas changes in response to variations in pressure when temperature and the amount of gas are held constant. Although most directly described by Boyle's Law (which assumes constant temperature), understanding this relationship is also part of the broader analysis in the combined gas law when temperature is allowed to vary.

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