The First Law of Thermodynamics for Closed Systems: Derivation and Sample Problems

Abstract

The material presented in this lecture is adapted from Chapter 3 of T&M. First, we will discuss mechanical work done on a rigid body. We will also introduce other types of work, including surface, electric, and magnetic. Second, we will extend the concept of mechanical work done on a rigid body to that associated with a thermodynamic system, for example, work done by a gas expanding against the atmosphere in a cylinder-piston assembly in the presence of friction. Third, we will discuss a key result that the work done by a system on the environment is equal to minus the work done by the environment on the system. We will stress that work is a mode of energy transfer which exists only at the boundary between a system and the environment. In the system or in the environment, there is only energy, which we will introduce through Postulate III as work done on the system under adiabatic conditions. Fourth, we will introduce heat absorbed by the system as the difference between the work done on the system under adiabatic conditions and the actual work done on the system. Like work, heat is a form of energy transfer which exists solely at the boundary between the system and the environment. Fifth, after we introduce work, energy, and heat, the First Law of Thermodynamics for a closed system will emerge naturally. Finally, we will solve Sample Problems 3.1, 3.2, and 3.3 to help crystallize the material taught.