A 1.00 -mol sample of an ideal monatomic gas, initially at a...

A 1.00 -mol sample of an ideal monatomic gas, initially at a pressure of 1.00 $\mathrm{atm}$ and a volume of $0.0250 \mathrm{m}^{3},$ is heated to a final state with a pressure of 2.00 $\mathrm{atm}$ and a volume of $0.0400 \mathrm{m}^{3} .$ Determine the change in entropy of the gas in this process.

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Key Concepts

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, relates the pressure, volume, and temperature of an ideal gas. This fundamental equation allows one to determine any one variable if the others are known, and is essential when analyzing state changes in gases.

State Functions

Entropy is a state function, meaning that its change depends only on the initial and final states of a system, and not on the path taken between them. This property allows the calculation of entropy change for a process by considering any convenient reversible path between the same states.

Entropy Change in Reversible Processes

For reversible processes involving an ideal gas, the entropy change can be calculated using an expression that accounts for changes in temperature and volume. This typically takes the form ?S = nC? ln(T?/T?) ? nR ln(P?/P?) or ?S = nC? ln(T?/T?) + nR ln(V?/V?), depending on the known quantities, where C? and C? are the heat capacities at constant pressure and volume, respectively.

Heat Capacities for a Monatomic Ideal Gas

Monatomic ideal gases have specific heat capacities, with C? = (3/2)R and C? = (5/2)R, where R is the gas constant. These values are crucial when computing the change in entropy or internal energy during processes involving monatomic gases.

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