One mole of an ideal gas at 25^∘ C expands in volume from 1.0 L to 4.0 L at constant . tempera

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One mole of an ideal gas at 25^∘ C expands in volume from...

One mole of an ideal gas at $25^{\circ} \mathrm{C}$ expands in volume from $1.0 \mathrm{~L}$ to $4.0 \mathrm{~L}$ at constant . temperature. What work (in $J$ ) is done if the gas expands against vacuum $\left(P_{\text {cxtemal }}=0\right)$ ? (a) $-4.0 \times 10^{2}$ (b) $-3.0 \times 10^{2}$ (c) $-1.0 \times 10^{2}$ (d) Zero

One mole of an ideal gas at $25^{\circ} \mathrm{C}$ expands in volume from $1.0 \mathrm{~L}$ to $4.0 \mathrm{~L}$ at constant . temperature. What work (in $J$ ) is done if the gas expands against vacuum $\left(P_{\text {cxtemal }}=0\right)$ ?
(a) $-4.0 \times 10^{2}$
(b) $-3.0 \times 10^{2}$
(c) $-1.0 \times 10^{2}$
(d) Zero

Key Concepts

Ideal Gas

An ideal gas is a hypothetical gas that follows the ideal gas law, where the behavior of the gas particles is simplified by assuming no intermolecular forces and that the particles occupy no volume. This model is fundamental in thermodynamics because it allows for the prediction of gas behavior under various conditions such as changes in temperature, pressure, and volume.

Isothermal Process

An isothermal process is one in which the temperature of the system remains constant throughout the process. For an ideal gas in an isothermal process, any work done by or on the gas is exactly balanced by heat transfer in or out of the system to maintain a constant temperature, according to the first law of thermodynamics.

Work in Thermodynamic Processes

In thermodynamics, work is defined as the energy transfer due to a force acting over a distance, or more specifically, during a volume change it is given by the integral of pressure with respect to volume. The calculation of work depends on the nature of the process, such as whether the pressure remains constant, variable, or is effectively zero in cases like free expansion.

Free Expansion

Free expansion refers to a process in which a gas expands into a vacuum without any opposing external pressure. In such a scenario, since there is no external pressure to do work against, no work is done by the gas despite the change in volume. This is a specific type of process that highlights the relationship between external forces and the work performed during gas expansion.

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