Why is PV Included in the Enthalpy Equation HU PV?

Introduction

The concept of enthalpy, denoted by h, is central to thermodynamics and is often expressed as the sum of internal energy (u) and the product of pressure (p) and volume (v):

Understanding Enthalpy:

1. Definition and Significance:

The equation H U PV, where H represents the change in enthalpy, U the change in internal energy, and PV the pressure-volume work, is fundamental in thermodynamics. This equation highlights the fact that heat added to a system can be used to either increase the internal energy or to perform external work, such as pressure-volume (PV) work.

2. Components of Enthalpy:

This definition is crucial because not all aspects of heat transfer can be directly measured. While the change in internal energy can be quantified, the total heat added to a system is not solely used to increase the internal energy; some of it goes into performing external work (PV work). Therefore, it is the change in enthalpy, rather than the change in internal energy alone, that is typically used in thermodynamic calculations.

3. Constant Pressure Conditions:

Many chemical reactions occur at constant pressure, such as those in the atmosphere or in aqueous solutions. Under these conditions, the work done by the system during a process is directly related to the change in volume and the external pressure:

W PV

Substituting this into the enthalpy equation, we obtain:

H U PV

Explanation of the Terms:

1. Internal Energy (U):

U represents the energy of the system when no external work is performed. It is a state function, meaning it is determined solely by the current state of the system.

2. Pressure-Volume Work (PV):

PV represents the work done by the system during expansion against an external pressure. This component of the enthalpy equation allows us to account for the energy transferred as work done by the system.

3. Enthalpy Change (ΔH):

The change in enthalpy, ΔH, is defined as the sum of the change in internal energy and the work performed in the form of pressure-volume work:

ΔH ΔU PΔV

ΔH can also be related to heat flow during a chemical reaction, and is a more convenient quantity to measure than the change in internal energy alone, especially under constant pressure conditions.

PV as a Form of Energy:

1. Units and Energy Density:

The term PV has units of Joules, which is the standard unit of energy. Pressure (P) is measured in Pascals (Pa), and volume (V) in cubic meters (m3). When multiplied, the result is:

Pa * m3 N/m2 * m3 N * m Joules (J)

PV represents the stored energy in the form of pressure over a given volume. This energy is available to perform external work.

2. Potential Work:

This term, PV, can be considered as potential work, meaning the energy that is stored in the system due to its state of being under pressure and occupying a certain volume.

3. Equations and Relationships:

The relationship between enthalpy, internal energy, and pressure-volume work is summarized by the equations:

Q ΔU W

Example:

When a gas expands at constant pressure, the work done is given by:

W PV

Substituting this into the enthalpy equation:

ΔH ΔU W ΔU PV

and under constant pressure:

ΔH ΔU PΔV Q

This confirms that the change in enthalpy is equivalent to the heat flow (Q) during a chemical reaction at constant pressure.

Conclusion:

The inclusion of PV in the enthalpy equation serves as a bridge between the change in internal energy and the work done by the system during expansion. This makes ΔH a particularly useful quantity for understanding and calculating heat flow in chemical reactions under constant pressure conditions.