CHEMISTRY · Multi-part · AP · Chemistry · Thermodynamics and Electrochemistry · Thermodynamics and Electrochemistry
Problem
For an ideal gas undergoing a reversible, isothermal process, the entropy change can be expressed in terms of either volume or pressure. Consider a sample of ideal gas that is initially at pressure P1 and volume V1 and undergoes a reversible, isothermal expansion to pressure P2 and volume V2 at temperature T.
(a) Starting from the ideal‐gas law and the definition of entropy, derive an expression for the molar entropy change, ΔSˉ, in terms of the initial and final pressures, P1 and P2, only.
(b) Show algebraically that the expression you derived in part (a) is equivalent to the more familiar form that contains ln(V1V2). Clearly state the mathematical step that makes the two forms identical.
(c) Liquid nitrogen is vaporized and warmed to 300 K, forming 0.800 mol of gaseous N2 at 1.00 atm that then undergoes a reversible, isothermal compression to 5.00 atm. Using the expression you derived in part (a), calculate the entropy change of the nitrogen gas during the compression.
(d) Discuss qualitatively whether your numerical answer in part (c) would change if the same compression were performed irreversibly but with the same initial and final states. Support your discussion with thermodynamic reasoning.