If the balloon rises quickly, so that no heat transfer is...

If the balloon rises quickly, so that no heat transfer is possible, the temperature inside the balloon will drop as the gas expands. If a $4.0 \mathrm{~m}^{3}$ balloon is launched at a pressure of $100 \mathrm{kPa}$ and rapidly rises to a point where the pressure is $50 \mathrm{kPa}$, the volume of the balloon will be A. Greater than $8.0 \mathrm{~m}^{3}$ B. $8.0 \mathrm{~m}^{3}$ C. Less than $8.0 \mathrm{~m}^{3}$

If the balloon rises quickly, so that no heat transfer is possible, the temperature inside the balloon will drop as the gas expands. If a $4.0 \mathrm{~m}^{3}$ balloon is launched at a pressure of $100 \mathrm{kPa}$ and rapidly rises to a point where the pressure is $50 \mathrm{kPa}$, the volume of the balloon will be
A. Greater than $8.0 \mathrm{~m}^{3}$
B. $8.0 \mathrm{~m}^{3}$
C. Less than $8.0 \mathrm{~m}^{3}$

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Key Concepts

Heat Transfer

Heat transfer involves the flow of thermal energy between a system and its environment. In the context of the rapid ascent of the balloon, the limited time for heat exchange means that the process is effectively adiabatic, causing the internal temperature to drop as the gas expands.

Adiabatic Process

An adiabatic process occurs when a gas expands or compresses without any heat exchange with its surroundings. This is particularly important in rapid processes, such as a balloon rising quickly, where the gas cools as it expands because no external heat is added.

Ideal Gas Law

The ideal gas law (PV = nRT) relates the pressure, volume, and temperature of a gas. It is pivotal in understanding how changes in pressure, such as those encountered by the rising balloon, are accompanied by shifts in volume and temperature, especially when heat transfer does not occur.

Pressure-Volume Relationship in Adiabatic Processes

In adiabatic processes, the relationship between pressure and volume is given by PV^? = constant, where ? is the specific heat ratio. This relationship highlights that the volume change is not simply the inverse of the pressure change due to the concurrent drop in temperature, resulting in a final volume that is less than what would be expected under isothermal conditions.

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