Types of Energies associated with Thermodynamic Processes - Thermodynamics - Mechanical

Overview

Energy appears in many forms in mechanics and thermodynamics. Some forms are macroscopic and directly measurable (for example, the energy due to the motion or position of a body). Other forms are microscopic - associated with the motion and interactions of atoms and molecules - and these form the principal consideration in thermodynamic analysis. When a thermodynamic system changes state, energy is exchanged with the surroundings as either heat or work, and the resulting change appears in one or more of the system's energy stores: internal energy, kinetic energy and potential energy. The following sections define and explain these forms, the customary sign conventions and how they are used in engineering thermodynamics.

Potential Energy (PE)

Potential energy is the macroscopic energy possessed by a body owing to its position in a force field (commonly the gravitational field near Earth). For a mass m located at elevation z measured from a chosen datum, the gravitational potential energy is given by:

PE = mgz      (1.2)

Here g is the acceleration due to gravity (g = 9.81 m/s²). Potential energy is a state function: its value depends on the position (z) of the system relative to the datum.

Kinetic Energy (KE)

Kinetic energy is the macroscopic energy possessed by a body due to its motion. For a body of mass m moving with speed u, the kinetic energy is

KE = 1/2 m u²      (1.3)

Kinetic energy is also a state function for a system at a given velocity. In many thermodynamic problems involving vessels or slow-moving systems, changes in macroscopic KE and PE are small compared with changes in internal energy and may be neglected. In flow processes (pumps, turbines, nozzles), KE changes can be important and must be included in the energy balance.

Internal Energy (Microscopic Forms of Energy)

Internal energy is the total microscopic energy of the matter in a system; it arises from motions and interactions at the atomic and molecular scale. Internal energy cannot be measured directly by macroscopic instruments, but it can be inferred from changes in macroscopic state variables (pressure, temperature, volume) and from heat and work interactions.

The microscopic contributions to internal energy include:

• Translational energy - kinetic energy of molecular translation (dominant for ideal gases).
• Rotational energy - molecular rotation about centre of mass (important for diatomic and polyatomic gases).
• Vibrational energy - molecular vibration modes (important at higher temperatures).
• Electronic energy - energy of electrons in atoms and molecules.
• Spin and nuclear energies - usually negligible for ordinary engineering thermodynamics.
• Intermolecular potential energy - attractive and repulsive forces between molecules; important in liquids and dense gases and in phase-change processes.
• Chemical bond energy - energy associated with chemical composition and reactions (chemical thermodynamics).

Because internal energy is a sum of these microscopic forms, it is a state function and is commonly denoted by U (or specific internal energy u = U/m). Changes in internal energy are central to thermodynamic analysis of heating, cooling, compression, expansion and chemical reactions.

Heat

Heat is the form of energy transferred across the boundary of a system due to a temperature difference between the system and its surroundings. Heat transfer always occurs from the region of higher temperature to the region of lower temperature. Heat is not a property of the system; it is energy in transit. By sign convention used here, heat entering the system is regarded as positive and heat leaving as negative.

Heat transfer may occur by conduction, convection and radiation. In thermodynamic energy accounting, the symbol Q (or q for specific heat) denotes heat transfer; Q is a path function and depends on how the process is carried out, not only on the end states.

Work

Work is energy transfer that results when a force acts through a distance as a macroscopic constraint on the system changes. Work can take many forms relevant to thermodynamic systems:

• Boundary (pressure-volume) work - work due to expansion or compression of the system boundary (piston, vessel walls).
• Shaft work - mechanical work transmitted by rotating shafts (turbines, compressors, stirrers).
• Electrical work - work associated with electrical currents and potentials.
• Magnetic and gravitational work - work due to magnetic or gravitational forces.
• Flow work - work required to push fluid into or out of a control volume (discussed further in the enthalpy section).

Like heat, work is a path function and cannot be stored as such in a system; after transfer, it appears as changes in state functions (U, KE, PE or chemical energy).

Boundary Work (Detailed)

Consider a piston-cylinder arrangement where a force F acts on the piston and produces a displacement x of the piston. The small amount of work associated with a differential displacement dx is

dW = F dx      (1.4)

If F is due to an external pressure P acting over piston area A (so F = P A), and the change in total volume of the system is dV^t = A dx, then

dW = P A dx

Substituting dV^t = A dx gives

dW = P dV^t

With the common engineering sign convention that work done on the system is positive, one often writes

dW = - P dV^t      (1.6)

Care must be taken with sign conventions: if the system expands against the surroundings, the system does work on the surroundings and the work term is negative in the above convention; if the surroundings compress the system, work is done on the system and the term is positive.

Fig. 1.2 Illustration of Thermodynamic Work

Enthalpy and Flow Work (Open Systems)

For steady flow processes in open systems (pumps, turbines, nozzles, heat exchangers), it is convenient to use the property enthalpy, because a portion of the energy transfer at inlet/outlet is the work required to push fluid into or out of the control volume. The enthalpy H is defined by:

H = U + P V

For specific quantities (per unit mass):

h = u + P v

Here u is the specific internal energy, v the specific volume and Pv represents the flow (or flow-work) term. In energy balances for open systems the combination h + 1/2 u² + g z is commonly used as the specific total energy (enthalpy plus kinetic and potential contributions).

State Functions and Path Functions

It is important to distinguish between state functions and path functions.

• State functions (examples: U, H, KE, PE, temperature, pressure) depend only on the current state of the system and not on how the system arrived there.
• Path functions (examples: Q and W) depend on the process path and cannot be assigned a unique value from the initial and final states alone.

Thermodynamic analysis uses state functions to quantify the storage of energy and path functions to quantify exchanges during processes.

Energy Accounting for a Closed System

The first law of thermodynamics for a closed system (no mass crossing the boundary) states that the change in the system's total energy equals heat supplied to the system minus work done by the system. In differential form:

ΔE = Q - W

Expressing total energy E as the sum of internal, kinetic and potential energies:

Δ(U + KE + PE) = Q - W

In many engineering problems the change in KE and PE can be neglected and the first law reduces to:

ΔU = Q - W

Energy Accounting for an Open (Flow) System

For steady-flow devices, the first law is written in terms of energy per unit mass and commonly uses enthalpy:

q̇ - ẇ = ṁ [(h₂ - h₁) + 1/2 (u₂² - u₁²) + g (z₂ - z₁)]

Here q̇ and ẇ are heat and shaft-work rates, ṁ is the mass flow rate, h is specific enthalpy and u and z are velocity and elevation.

Practical Remarks and Typical Approximations

• In many closed-system problems where the vessel is stationary and velocities are small, changes in KE and PE are negligible; energy analysis focuses on changes in internal energy (U) and boundary work.
• In flow problems, enthalpy h rather than internal energy u is used because it includes the flow work term P v needed to push fluid through inlets and outlets.
• Latent heat associated with phase change is a transfer of internal energy associated with changes in intermolecular potential energy; it appears as large changes in internal energy or enthalpy at nearly constant temperature for pure substances.
• Chemical reactions change the chemical (bond) component of internal energy; such energy change is handled by including chemical potential or formation enthalpies in the energy balance.

Examples of Where Each Energy Form Is Important

• Potential energy: pumped storage reservoirs, water distribution networks, calculating hydrostatic heads in pipes.
• Kinetic energy: flow in nozzles and diffusers, high-speed jets, energy losses in pipe flow conversions.
• Internal energy: heat addition in boilers, refrigeration cycles, combustion processes, phase changes.
• Enthalpy (flow work): turbines, compressors, heat exchangers, pumps - devices with steady mass flow.
• Work (shaft and boundary): engines, compressors, pistons, stirring devices.

Conclusion

Thermodynamic processes involve exchanges of energy in the forms of heat and work. The energy that can be stored in a system appears as internal energy (microscopic), kinetic energy and potential energy (macroscopic). For open systems, enthalpy conveniently combines internal and flow-work contributions. Correct use of sign conventions and clear identification of which energy terms are significant for a given problem are central to reliable energy balances and practical engineering design.

Notation and Symbols (summary)

• U - total internal energy (J)
• u - specific internal energy (J/kg)
• H - enthalpy (J)
• h - specific enthalpy (J/kg)
• KE - kinetic energy (J), KE = 1/2 m u²
• PE - potential energy (J), PE = mg z
• Q - heat transfer (J)
• W - work transfer (J)