Ideal Gas Law

Definition

The ideal gas law is a fundamental equation in thermodynamics that describes the relationship between the pressure, volume, amount of substance, and absolute temperature of an ideal gas. It is a macroscopic model that provides a simple way to predict the behavior of gases under various conditions.

5 Must Know Facts For Your Next Test

1. The ideal gas law is expressed as $PV = nRT$, where $P$ is the pressure, $V$ is the volume, $n$ is the amount of substance, $R$ is the universal gas constant, and $T$ is the absolute temperature.
2. The ideal gas law assumes that gas molecules are point-like particles that do not interact with each other, except during perfectly elastic collisions.
3. The ideal gas law is a simplified model that works well for gases at low pressures and high temperatures, but deviations from this model occur at higher pressures and lower temperatures.
4. The universal gas constant, $R$, has a value of approximately $8.314 \ ext{J/mol} \. \text{K}$, and its value is the same for all ideal gases.
5. The ideal gas law can be used to calculate various properties of a gas, such as density, molar mass, and the work done by or on the gas during a process.

Review Questions

• Explain how the ideal gas law relates to the first law of thermodynamics and the concepts of thermal energy and work.
  • The first law of thermodynamics states that the change in the internal energy of a system is equal to the sum of the work done on the system and the heat added to the system. The ideal gas law provides a way to relate the changes in pressure, volume, and temperature of a gas to the work done and the thermal energy exchanged. For example, if a gas expands against a constant external pressure, the work done by the gas is given by the product of the pressure and the change in volume, as described by the ideal gas law. Similarly, if a gas is heated at constant volume, the change in internal energy is related to the change in temperature through the ideal gas law.
• Describe how the assumptions of the ideal gas model affect the relationship between the variables in the ideal gas law.
  • The ideal gas law assumes that gas molecules are point-like particles that do not interact with each other, except during perfectly elastic collisions. This means that the only forces acting on the gas molecules are those due to their collisions with the container walls, and there are no significant intermolecular forces. As a result, the pressure, volume, and temperature of the gas are related in a simple, linear way, as described by the ideal gas law. If the assumptions of the ideal gas model are not met, such as at high pressures or low temperatures, the relationship between the variables becomes more complex, and deviations from the ideal gas law are observed.
• Analyze how the ideal gas law can be used to calculate the work done by or on a gas during a thermodynamic process, and explain how this relates to the first law of thermodynamics.
  • The ideal gas law can be used to derive an expression for the work done by or on a gas during a thermodynamic process. Specifically, the work done is equal to the negative of the integral of the pressure with respect to the volume, which can be expressed using the ideal gas law as $W = -\int PdV = -nRT\int \frac{dV}{V}$. This work term appears in the first law of thermodynamics, which states that the change in internal energy of a system is equal to the sum of the work done on the system and the heat added to the system. By using the ideal gas law to calculate the work term, the first law can be applied to analyze the energy transformations occurring in an ideal gas system, such as the conversion between thermal energy and mechanical work.

Related terms

Pressure:

The force exerted per unit area on the walls of a container by the gas molecules.

Volume:

The space occupied by the gas within a container.

Absolute Temperature:

The temperature of a gas measured on the Kelvin scale, which has a lower limit of absolute zero.