Two balloons are inflated at the same temperature to the...

Two balloons are inflated at the same temperature to the same volume (Figure $\mathrm{P} 17.1$ ), though it takes more gas to inflate the balloon on the right. In which balloon is the gas under greater internal pressure? In which balloon does the gas have greater entropy? (FIGURE CAN'T COPY)

Key Concepts

Ideal Gas Law

The Ideal Gas Law (pV = nRT) relates pressure (p) to the number of moles (n), volume (V), and temperature (T) of a gas. When temperature and volume are held constant, the pressure inside a container increases with the number of gas molecules. Thus, adding more gas (i.e. increasing n) leads directly to a higher internal pressure.

Internal Pressure

Internal pressure in a gas is the force per unit area that the gas molecules exert on the walls of their container due to collisions. With a fixed volume and temperature, a larger number of molecules results in more frequent and forceful collisions, which raises the internal pressure. This concept is directly applied by comparing systems with different amounts of gas.

Entropy

Entropy is a measure of the number of microstates available to a system and thus its level of disorder or randomness. For an ideal gas at constant temperature and volume, the entropy per molecule depends on the free volume available to each molecule. When more gas molecules are present in the same volume, each molecule has less available space, resulting in a lower entropy per molecule, even though the total entropy (being an extensive property) scales with the total number of molecules.

Extensive versus Intensive Properties

In thermodynamics, extensive properties (like total entropy) depend on the size or amount of substance, while intensive properties (like pressure) do not. In the context of these balloons, although the balloon with more gas has a greater total number of molecules (an extensive property), it exhibits higher internal pressure (an intensive property) and a lower entropy per molecule due to the reduced available volume per molecule.

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