One mole of an ideal gas undergoes an isothermal reversible...

One mole of an ideal gas undergoes an isothermal reversible expansion at $25^{\circ} \mathrm{C} .$ During this process, the system absorbs $855 \mathrm{J}$ of heat from the surroundings. When this gas is compressed to the original state in one step (isothermally), twice as much work is done on the system as was performed on the surroundings in the expansion. a. What is $\Delta S$ for the one-step isothermal compression? b. What is $\Delta S_{\text {univ }}$ for the overall process (expansion and compression)?

One mole of an ideal gas undergoes an isothermal reversible expansion at $25^{\circ} \mathrm{C} .$ During this process, the system absorbs $855 \mathrm{J}$ of heat from the surroundings. When this gas is compressed to the original state in one step (isothermally), twice as much work is done on the system as was performed on the surroundings in the expansion.
a. What is $\Delta S$ for the one-step isothermal compression?
b. What is $\Delta S_{\text {univ }}$ for the overall process (expansion and compression)?

Key Concepts

System and Surroundings

In thermodynamic analyses, the system refers to the part of the universe under study while the surroundings encompass everything else. Understanding the interplay of energy and entropy changes between the system and the surroundings is critical for applying the laws of thermodynamics, particularly in assessing the overall impact on the universe in any process.

Ideal Gas

An ideal gas is a theoretical construct in which the gas particles interact only through elastic collisions and obey the ideal gas law (PV = nRT). This assumption simplifies thermodynamic calculations by neglecting intermolecular forces and the finite volume of particles, making it easier to predict the behavior of gases in various processes.

Isothermal Process

An isothermal process is one in which the temperature of the system remains constant throughout the transformation. In such a process for an ideal gas, the internal energy remains unchanged, meaning that any heat added to or removed from the system is exactly balanced by the work done by or on the system.

Reversible Process

A reversible process is an idealized process that occurs infinitely slowly so that the system remains in thermodynamic equilibrium at all stages. This concept is important because, in a reversible process, the change in entropy is precisely defined and the process can be reversed without any net change in the entropy of the universe.

Entropy Change

Entropy change is a measure of the degree of disorder or randomness in a system, formally defined for a reversible process as the integral of the infinitesimal heat transfer divided by the temperature (dQ/T). It is a central concept in thermodynamics, used to determine the direction of spontaneous processes and to assess the efficiency of thermodynamic cycles.

Second Law of Thermodynamics

The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time; it either increases or remains constant in ideal reversible processes. This principle governs the direction of natural processes and is fundamental in evaluating the feasibility and irreversibility of thermodynamic transformations.

Work and Heat Exchange

Work and heat are the two primary forms of energy transfer in thermodynamic processes. In an isothermal process involving an ideal gas, work done by or on the system is directly related to the heat exchanged because the internal energy remains constant. This relationship is derived from the first law of thermodynamics, which relates changes in internal energy to work done and heat transfer.

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