Suppose 5.00 moles of an ideal monatomic gas expands at a...

Suppose 5.00 moles of an ideal monatomic gas expands at a constant temperature of $22.0^{\circ} \mathrm{C}$ from an initial volume of $2.00 \mathrm{~m}^{3}$ to $8.00 \mathrm{~m}^{3}$.
a) How much work is done by the gas?
b) What is the final pressure of the gas?

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Key Concepts

Ideal Gas Law

The ideal gas law (PV = nRT) provides a relationship among the pressure, volume, temperature, and number of moles of a gas. It is a fundamental equation used to describe the behavior of ideal gases and forms the basis for analyzing processes that the gas undergoes.

Isothermal Process

An isothermal process is characterized by a constant temperature throughout the process. In such a process, the internal energy of an ideal gas remains unchanged, and changes in work are solely due to changes in volume.

Work in Isothermal Expansion

In an isothermal expansion of an ideal gas, the work done by the gas is calculated by the integral of pressure with respect to volume, which using the ideal gas law results in the expression W = nRT ln(V_final/V_initial). This formula quantifies the energy transfer as work during the expansion.

Pressure-Volume Relationship in Isothermal Conditions

Under isothermal conditions, the pressure and volume of an ideal gas are inversely related (as stated by Boyle's Law). Since the product of pressure and volume remains constant, knowing the change in volume allows one to determine the new pressure when either the initial pressure or volume is known.

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