Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
A Quasi-static process is an idealized process that occurs so slowly that the system remains in thermal and mechanical equilibrium with its surroundings at every instant.
An Isothermal Process is a thermodynamic process in which the temperature of the system remains constant (). For an ideal gas, the change in internal energy is zero (), and the process follows Boyle's Law: .
An Adiabatic Process is one in which there is no exchange of heat between the system and the surroundings (). This usually happens when the system is thermally insulated or the process is very fast. It follows the relation .
An Isobaric Process occurs at constant pressure (). The work done is and the heat supplied is used to change both internal energy and perform work.
An Isochoric Process occurs at constant volume (). Since there is no change in volume, the work done . By the first law, all heat supplied goes into increasing the internal energy: .
The First Law of Thermodynamics is a statement of conservation of energy: , where is heat supplied, is change in internal energy, and is work done by the system.
📐Formulae
💡Examples
Problem 1:
Calculate the work done when of a gas expands isothermally at to double its original volume. (Given and )
Solution:
Given: , , . Using the isothermal work formula:
Explanation:
Since the process is isothermal, we use the natural log formula for work. Temperature must be converted to Kelvin.
Problem 2:
A gas at initial pressure is compressed suddenly to th of its initial volume. Find the final pressure.
Solution:
For a sudden compression, the process is adiabatic. We use:
Explanation:
The 'sudden' nature implies an adiabatic process. We apply the Poisson's relation to find the ratio of pressures.