A gas with initial state variables p₁, V₁, and T₁ expands isothermally until V₂=2V₁. What are (a) T₂

Verified step by step guidance

1. Identify that the process is isothermal, which means the temperature remains constant throughout the process. Therefore, T₂ = T₁.
2. Since the volume doubles during the isothermal expansion (V₂ = 2V₁), use the ideal gas law, PV = nRT, to analyze the changes in other state variables.
3. Recognize that the number of moles (n) and the gas constant (R) are constants, and thus, the product PV remains constant for an isothermal process.
4. Set up the equation for the initial state and the final state using the ideal gas law: P₁V₁ = P₂V₂.
5. Substitute V₂ = 2V₁ into the equation and solve for P₂ to see how the pressure changes.

Key Concepts

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 the gas does not change. In this scenario, since the gas expands isothermally, the temperature T₂ will equal the initial temperature T₁.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in thermodynamics that relates the pressure (p), volume (V), and temperature (T) of an ideal gas. It is expressed as PV = nRT, where n is the number of moles and R is the ideal gas constant. This law helps in understanding how changes in volume and temperature affect the pressure of a gas, particularly in isothermal conditions.

Charles's Law

Charles's Law states that the volume of a gas is directly proportional to its temperature when pressure is held constant. This relationship implies that if the volume of a gas increases, its temperature must also increase, provided the pressure does not change. In the context of an isothermal expansion, while the volume increases, the temperature remains constant, reinforcing the idea that T₂ = T₁.