Suppose 0.05839 mole of an ideal monatomic gas has a...

Suppose 0.05839 mole of an ideal monatomic gas has a pressure of 1.000 atm at $273.15 \mathrm{~K}$ and is then cooled at constant pressure until its volume is reduced by $47.11 \% .$ What is the amount of work done by the gas?

Key Concepts

Work in Thermodynamic Processes

Work in thermodynamic processes involving gases is typically calculated by integrating the pressure with respect to volume change. For processes at constant pressure (isobaric), the work done by the gas is given by the product of the constant pressure and the change in volume (W = P?V). This concept helps in determining the energy transferred as work when a gas expands or is compressed.

Sign Conventions for Work

The sign convention for work in thermodynamics indicates that work done by the system on the surroundings is considered positive, while work done on the system is negative. This is important when calculating and interpreting results, as a decrease in volume (compression) will result in work done by the surroundings on the gas, affecting the sign and magnitude of the work term.

Ideal Gas Law

The ideal gas law describes the relationship between pressure, volume, number of moles, and temperature in a gas (PV = nRT). It is a fundamental equation in thermodynamics that allows us to predict how a gas will respond to changes in any of these properties while holding the others constant. This concept is crucial when determining initial or final states of a gas in problems involving processes like heating, cooling, or compression.

Isobaric Process

An isobaric process is one in which the pressure remains constant while other state variables like volume and temperature change. In such processes, the relationship between volume and temperature is directly described by Charles’s law, and understanding this concept is key to analyzing the behavior of gases under constant pressure, including calculating work done during expansion or compression.

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