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

A sample consisting of $n$ mol of an ideal gas undergoes a reversible isobaric expansion from volume $V_{i}$ to volume $3 V_{i} .$ Find the change in entropy of the gas by calculating $\int_{i}^{f} d Q / T$ where $d Q=n C_{P} d T .$

Key Concepts

Heat Capacity at Constant Pressure

The heat capacity at constant pressure (Cp) is a property that represents the amount of heat required to raise the temperature of a substance by one degree while maintaining a constant pressure. Cp is crucial in an isobaric process because it directly links the heat added to the system with the resulting change in temperature, which is then used to calculate changes in entropy.

Entropy Change

Entropy change quantifies the degree of disorder or randomness in a system as it undergoes a thermodynamic process. For a reversible process, the change in entropy is calculated by integrating the differential heat transfer divided by temperature (dQ/T), serving as a fundamental measure of energy dispersal in the system.

Reversible Process

A reversible process is an idealized thermodynamic change that occurs infinitely slowly, ensuring that the system is always in equilibrium. In such processes, every stage can be reversed without any net change in the system and surroundings, which is key for accurately calculating changes in state functions like entropy.

Ideal Gas

An ideal gas is a theoretical model in which gas particles are assumed to have no volume and do not interact with each other except through elastic collisions. This simplification allows the use of the ideal gas law (PV = nRT) to describe the behavior of gases, facilitating the analysis of thermodynamic processes.

Isobaric Process

An isobaric process is one that occurs at a constant pressure. This constraint simplifies the analysis of the process because the pressure remains unchanged even as other parameters like volume and temperature vary, and it allows the use of specific heat capacities to connect heat transfer with temperature change.

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