A sample consisting of n moles of an ideal gas undergoes a...

A sample consisting of $n$ moles of an ideal gas undergoes a reversible isobaric expansion from volume $V_{i}$ to volume $3 \bar{V}_{i}$ Find the change in entropy of the gas by calculating $\int_{i}^{\prime} d Q / T$ where $d Q=n C_{p} d T$

Key Concepts

Heat Capacity at Constant Pressure (Cp)

Heat capacity at constant pressure, Cp, is a measure of the amount of heat required to raise the temperature of a substance per unit temperature increase when the pressure is held constant. In thermodynamics, especially under isobaric conditions, Cp is used to calculate the heat transfer (dQ = n Cp dT) that directly influences the change in entropy during the process.

Ideal Gas Law

The ideal gas law, given by the equation PV = nRT, relates the pressure, volume, temperature, and the amount of an ideal gas. This relationship is fundamental in determining how a system behaves under various thermodynamic processes such as expansions and compressions. In problems involving entropy change, the ideal gas law is used to relate changes in volume to changes in temperature.

Entropy Change

Entropy is a measure of the dispersal of energy or the level of disorder within a system. In thermodynamics, the change in entropy during a reversible process is defined as the integral of the heat transfer divided by the temperature at which the transfer occurs. This concept is essential for understanding how energy is distributed during processes and is calculated using the definition ?S = ?(dQ/T).

Reversible Processes

A reversible process is an idealized process that happens infinitely slowly, ensuring that the system remains in equilibrium at every stage. This allows for the exact calculation of thermodynamic properties, such as changes in entropy, because the path taken by the process is well defined and the system can return to its original state without any net change in the universe.

Isobaric Process

An isobaric process is a thermodynamic process that occurs at constant pressure. Because the pressure remains fixed, other state variables such as volume and temperature are directly related by the ideal gas law. Understanding an isobaric process is crucial for determining the change in internal energy, work done by or on the system, and heat transferred, thus affecting the calculation of entropy change.

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