(a) What sign for ΔS do you expect when the pressure on...

(a) What sign for $\Delta S$ do you expect when the pressure on 0.600 mol of an ideal gas at $350 \mathrm{~K}$ is increased isothermally from an initial pressure of 0.750 atm? (b) If the final pressure on the gas is 1.20 atm, calculate the entropy change for the process. (c) Do you need to specify the temperature to calculate the entropy change? Explain.

Key Concepts

Isothermal Process

An isothermal process is one in which the temperature remains constant throughout. For an ideal gas, this means that any change in internal energy is zero, and the heat transfer into or out of the system is entirely used to do work. Understanding this concept is crucial because temperature constancy simplifies the relationships between pressure, volume, and entropy change in the gas.

Entropy Change for an Ideal Gas

The entropy change in an ideal gas during an isothermal process can be determined using the relation ?S = nR ln(V_final/V_initial) or equivalently ?S = nR ln(P_initial/P_final), where n is the number of moles and R is the ideal gas constant. This formula shows that if the gas is compressed isothermally (leading to a decrease in volume or an increase in pressure), the entropy of the system decreases.

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, links the pressure, volume, and temperature of an ideal gas. This law is fundamental in relating the state variables and is essential for converting changes in pressure to changes in volume when calculating the entropy change, particularly during processes where the temperature is held constant.

State Function

Entropy is a state function, which means its change depends only on the initial and final states of the system, not on the path taken between these states. This concept is key because it allows for the calculation of entropy change using any reversible path, even if the actual process followed is irreversible, provided the initial and final conditions are known.

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