Two tires shown in cross section in Figure P 12.3 are inflated at the same temperature to the sa

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Two tires shown in cross section in Figure P 12.3 are...

Two tires shown in cross section in Figure $\mathrm{P} 12.3$ are inflated at the same temperature to the same volume, though more air is used to inflate the tire on the right. In which tire is the gas under greater internal pressure and in which does the gas have greater entropy? (FIGURES CANT COPY)

Key Concepts

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental relation in thermodynamics that connects the pressure, volume, amount of gas (in moles), and temperature of an ideal gas. It explains how, for a fixed volume and temperature, an increase in the number of gas molecules (n) leads directly to an increase in pressure (P).

Internal Pressure

Internal pressure in a gas confined within a constant volume at a fixed temperature is governed by the number of gas molecules present. Since pressure is an intensive property, increasing the amount of gas (n) while keeping the volume and temperature constant results in greater internal pressure.

Entropy

Entropy is a measure of the disorder or randomness of a system and is an extensive property, meaning it scales with the size or amount of material in the system. For a gas, adding more molecules increases the number of possible microstates, thereby raising the overall entropy even when the temperature and volume are unchanged.

Extensive and Intensive Properties

Understanding the difference between extensive and intensive properties is crucial in thermodynamics. Intensive properties, like pressure, do not depend on the amount of substance present, whereas extensive properties, like entropy, do depend on the quantity of material. This distinction helps explain why two systems at the same temperature and volume can have different pressures and entropies if the number of gas molecules differs.

Transcript

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