# 2: The First Law

• 2.1: Internal Energy
In order to study the exchange of energy between a system and its surroundings, we need to define the boundaries of the system. We then need to determine how much energy the system possesses. This energy is known as the total energy of the system or the internal energy of the system. In this section, we will describe the basic parameters of the system, distinguish between heat and work, define internal energy, and determine changes in the internal energy.
• 2.2: Enthalpy
Enthalpy is defined as the sum of the internal energy and the product of the pressure times the volume: H = U + PV. Many experimental studies of enthalpy occur at constant pressure, under which conditions it can be shown that the change in enthalpy is the change in heat. In this section we will derive the relationship between enthalpy and heat, and then describe constant-pressure calorimetry experiments, introduce molar heat capacity at constant pressure, and then relate the constant-pressure an
• 2.3: Thermochemistry
Thermochemistry is an extremely useful application of thermodynamics because it allows us to use previously gathered data to estimate the enthalpy changes of processes that we have not yet done, or that are unknown to us. The two most common applications are the use of Hess's Law to combine the enthalpy changes of entire chemical equations, and the combination of the enthalpy changes of formation of the pure substances involved in a process.
• 2.4: State Functions and Exact Differentials
Internal energy and enthalpy are state functions, meaning that the changes in their values as we move the system from state 1 to state 2 do not depend on how we changed the system from state 1 to state 2. State functions have vastly different mathematical properties than path-dependent functions, and we will investigate some of the mathematical properties of state functions in this section.
As noted in Topic 2A, an adiabatic change is a change that occurs with no transfer of heat. In other words, under adiabatic conditions $$q =0$$ and $$\Delta U = w_{ad}$$. In this section, we will derive formulas to calculate the changes in temperature and the changes in pressure that occur during adiabatic changes.

Thumbnail: A thermite reaction using iron(III) oxide. The sparks flying outwards are globules of molten iron trailing smoke in their wake. Image used with permission (CC SA-BY 3.0; Nikthestunned)