A unit mass of an ideal gas at temperature T undergoes a...

A unit mass of an ideal gas at temperature $T$ undergoes a reversible isothermal process from pressure $P_{1}$ to pressure $P_{2}$ while losing heat to the surroundings at temperature $T$ in the amount of $q .$ If the gas constant of the gas is $R,$ the entropy change of the gas $\Delta s$ during this process is (a) $\Delta s=R \ln \left(P_{2} / P_{1}\right)$ (b) $\Delta s=R \ln \left(P_{2} / P_{1}\right)-q / T$ (c) $\Delta s=R \ln \left(P_{\mathrm{J}} / P_{2}\right)$ (d) $\Delta s=R \ln \left(P_{1} / P_{2}\right)-q / T$ (e) $\Delta s=0$

A unit mass of an ideal gas at temperature $T$ undergoes a reversible isothermal process from pressure $P_{1}$ to pressure $P_{2}$ while losing heat to the surroundings at temperature $T$ in the amount of $q .$ If the gas constant of the gas is $R,$ the entropy change of the gas $\Delta s$ during this process is
(a) $\Delta s=R \ln \left(P_{2} / P_{1}\right)$
(b) $\Delta s=R \ln \left(P_{2} / P_{1}\right)-q / T$
(c) $\Delta s=R \ln \left(P_{\mathrm{J}} / P_{2}\right)$
(d) $\Delta s=R \ln \left(P_{1} / P_{2}\right)-q / T$
(e) $\Delta s=0$

Key Concepts

Heat Transfer in Thermodynamics

Heat transfer is the mechanism by which energy is exchanged between a system and its surroundings. In reversible isothermal processes, the relationship between heat transfer and entropy change is particularly straightforward, with the entropy change being equal to the heat exchanged divided by the constant process temperature. This relationship is central to analyzing energy balances in thermodynamic processes.

Entropy Change

Entropy is a state function that quantifies the degree of disorder or randomness in a system. The change in entropy during a process, especially a reversible process, is calculated by the integral of the reversible heat transfer divided by temperature. Understanding how entropy is exchanged during processes is key to applying the second law of thermodynamics.

Isothermal Process

An isothermal process is one that occurs at a constant temperature. For an ideal gas undergoing such a process, the internal energy remains constant since it is a function of temperature only. This implies that any work done by or on the gas is exactly balanced by heat transfer, forming a basis for further analysis using thermodynamic relationships.

Reversible Process

A reversible process is an idealized process that proceeds infinitely slowly such that the system remains in thermodynamic equilibrium at all times. In reversible processes, the entropy change of the system can be directly related to the heat exchanged divided by the temperature, ensuring maximum work extraction or minimum work input under given conditions.

Ideal Gas

An ideal gas is a theoretical gas composed of a large number of randomly moving, non-interacting point particles. The behavior of an ideal gas is well described by the ideal gas law, which relates pressure, volume, and temperature. This simplification allows for clear mathematical descriptions of thermodynamic processes and is fundamental to understanding energy exchanges in many systems.

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