An ideal gas in a cylinder fitted with a piston expands at...

An ideal gas in a cylinder fitted with a piston expands at constant temperature from a pressure of 5 atm and a volume of $6.0 \mathrm{~L}$ to a final volume of $12 \mathrm{~L}$ against a constant opposing pressure of 2.5 atm. How much heat does the gas absorb, expressed in units of $L$ atm (liter $\times$ atm)? (Hint: See Exercise 18.121.)

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Key Concepts

Ideal Gas

An ideal gas is a theoretical gas composed of many randomly moving point particles that interact only through elastic collisions. The behavior of an ideal gas is well described by the ideal gas law, which relates pressure, volume, and temperature, and is essential for understanding gas expansion and compression processes.

Isothermal Process

An isothermal process is one in which the temperature of the system remains constant. For an ideal gas undergoing an isothermal process, the internal energy remains unchanged, meaning that any heat added to the system is exactly balanced by the work done by the gas.

Thermodynamic Work

Thermodynamic work in the context of a gas expansion is defined as the force applied over a distance, or equivalently, for gases, the product of pressure and change in volume. When a gas expands against a constant external pressure, the work done is simply the external pressure multiplied by the change in volume.

First Law of Thermodynamics

The first law of thermodynamics states that the change in the internal energy of a system is equal to the heat added to the system minus the work done by the system. For an isothermal process of an ideal gas, the internal energy change is zero, so the heat absorbed by the gas is equal to the work done by the gas during expansion.

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