A weather balloon is inflated to a volume of 28.5 L at a pressure of 748 mmHg 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 $748 \mathrm{mmHg}$ and a temperature of $28.0^{\circ} \mathrm{C}$. The balloon rises in the atmosphere to an altitude of approximately 25,000 feet, where the pressure is $385 \mathrm{mmHg}$ 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 combines Boyle's Law, Charles's Law, and Gay-Lussac's Law into one expression: (P1V1)/T1 = (P2V2)/T2. It is used to relate the pressure, volume, and temperature of an ideal gas when the amount of gas remains constant. This law allows the calculation of any missing variable when the state of a gas changes due to varying environmental conditions.

Temperature Conversion

Temperature in gas law problems must be expressed in an absolute scale (Kelvin) because the laws of thermodynamics are based on absolute temperature. Converting Celsius to Kelvin (by adding 273.15) ensures that the temperature values used in calculations are consistent with the requirements of the gas equations.

Gas Expansion Due to Pressure and Temperature Changes

Gas expansion or compression occurs when there is a change in external conditions such as pressure and temperature. When a gas moves to an environment with lower pressure or experiences a temperature change, its volume adjusts according to the gas laws, which is essential in predicting behavior in applications like weather balloons.

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