An ideal gas is enclosed in a cylinder with a movable piston...

An ideal gas is enclosed in a cylinder with a movable piston on top of it. The piston has a mass of $8.00 \times 10^{3} \mathrm{g}$ and an area of 5.00 $\mathrm{cm}^{2}$ and is free to slide up and down, keeping the pressure of the gas constant. (a) How much work is done on the gas as the temperature of 0.200 $\mathrm{mol}$ of the gas is raised from $20.0^{\circ} \mathrm{C}$ to $3.00 \times 10^{2 \circ} \mathrm{C}$ ? (b) What does the sign of your answer to part (a) indicate?

Key Concepts

Work in Thermodynamic Processes

In thermodynamics, work is defined as the energy transfer that results from a change in volume under pressure. For a constant pressure process, the work done by or on the gas is given by W = P × ?V. This concept is crucial since it quantifies the energy exchange between a system and its surroundings during expansion or compression.

Sign Conventions for Work

The sign of work in thermodynamics indicates the direction of energy transfer. Conventionally, work done by the system (such as during expansion) is considered negative, meaning the system loses energy to the surroundings, while work done on the system (such as during compression) is positive. This convention is essential for correctly applying the first law of thermodynamics and understanding how processes affect a system's internal energy.

Ideal Gas Law

This law, expressed as PV = nRT, relates the pressure, volume, and temperature of an ideal gas. It forms the cornerstone of understanding how gases behave under various conditions, allowing predictions of how changes in one state variable affect the others while assuming the gas particles do not interact significantly and occupy negligible volume.

Constant Pressure (Isobaric) Process

An isobaric process is one in which the pressure remains constant, meaning any heat added to or removed from the system results in a change in its volume and temperature. In such a process, the volume variation can be directly tied to the change in temperature using the ideal gas law, and work is calculated as the product of the constant pressure and the change in volume.

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