An ideal gas undergoes a reversible isothermal expansion at 77.0^∘ C, increasing its volume from

step 1 So here we're going to evaluate the number of moles in this isothermal process. An isothermal pr

An ideal gas undergoes a reversible isothermal expansion at...

An ideal gas undergoes a reversible isothermal expansion at $77.0^{\circ} \mathrm{C},$ increasing its volume from $1.30 \mathrm{~L}$ to $3.40 \mathrm{~L}$. The entropy change of the gas is $22.0 \mathrm{~J} / \mathrm{K}$. How many moles of gas are present?

Key Concepts

Ideal Gas Behavior

Ideal gas behavior is governed by the ideal gas law, which relates pressure, volume, temperature, and the amount of gas. This assumption simplifies the analysis by neglecting intermolecular forces and the volume occupied by the gas molecules, making it easier to apply thermodynamic equations.

Entropy

Entropy is a thermodynamic state function that quantifies the degree of disorder or randomness in a system. It measures how energy is dispersed at a given temperature and plays a crucial role in determining the spontaneity and directionality of thermodynamic processes, as described by the Second Law of Thermodynamics.

Isothermal Process

An isothermal process is one in which the system’s temperature remains constant throughout. In such processes, for an ideal gas, the internal energy remains unchanged, and any work performed by or on the system is exactly offset by heat exchange with the surroundings.

Reversible Process

A reversible process is an idealized, infinitely slow process that maintains the system in thermodynamic equilibrium at all times. This concept allows for maximum work output or input and helps establish benchmark relations, such as those used in ideal entropy calculations.

Entropy Change in Isothermal Expansion

For an ideal gas undergoing a reversible isothermal expansion, the change in entropy can be expressed by the relation ?S = nR ln(V2/V1). This formula connects the macroscopic change in disorder (entropy change) to the microscopic parameters of the system, such as the number of moles and the change in volume.

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