n moles of an ideal gas at temperature T1 and volume V1 expand isothermally until the volume has doubled. In terms of n, T₁ , and V₁, what are (a) the final temperature,

Key Concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in thermodynamics that relates the pressure, volume, temperature, and number of moles of an ideal gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. This law is crucial for understanding the behavior of gases under various conditions.

Isothermal Process

An isothermal process is a thermodynamic process in which the temperature of the system remains constant. For an ideal gas, this means that any heat added to the system is used to do work, as the internal energy of an ideal gas depends only on temperature. In the context of the question, the gas expands isothermally, which implies that its temperature does not change despite the change in volume.

Thermodynamic Variables

Thermodynamic variables such as pressure, volume, and temperature are essential for describing the state of a gas. In this scenario, the initial state of the gas is defined by its temperature T1 and volume V1, while the final state after expansion will have a volume of 2V1. Understanding how these variables interact during an isothermal expansion helps in determining the final temperature and other properties of the gas.