Relationship Between Heat, Work, and Internal Energy

Have you ever wondered how a heat engine operates? What’s in a glass of water on the table, for example? When we look at a steady glass of water, we don’t see any kinetic or mechanical energy. However, when examined under a microscope, the internal energy is determined by the rapid motion of molecules. Thermodynamics is a branch of science concerned with the combined effects of heat, temperature, energy, and work on state transitions. Specific rules, known as thermodynamic laws, control these changes and their repercussions.

According to thermodynamic principles, heat energy created or absorbed in various chemical processes converts into various usable forms. We understand that we cannot create or destroy energy. We can only change it from one state to another. This principle is the bedrock of energy transformation, and its application in various fields represents an essential aspect of thermodynamics. Chemical reactions are also linked to different amounts of energy. The significance of thermodynamics is concerned with transferring energy from one form to another. It also looks into the relationship between heat and temperature and the relationship between energy and work.

After knowing what thermodynamics is, let’s discuss the relationship between internal energy, heat, and work.

Internal Energy

Both the total kinetic energy and potential energy contained inside the system are internal energy. Temperature, starting and ending states, but not the travel, affects internal energy. An ideal gas’s internal energy is entirely determined by temperature, whereas a real gas’s internal energy is determined by both temperature and volume.

The Joule is the unit of internal energy(J).

Heat

When temperature disparities occur, heat is the energy in transit. The internal energy combines internal kinetic energy due to molecular motion and internal potential energy due to attraction between molecular forces. A hot body has more internal energy than a cold one of the same size. The heat that enters the system is positive (+ve). The heat that escapes is regarded as a negative (-ve). The following elements influence the amount of heat flow:

• The substance’s weight (m).

• The difference in temperature between the two items (ΔT).

• And last, the substance’s nature.

Work

Work performed by a system is defined as the energy transferred by the system to its surroundings in thermodynamics. Work is an energy form, but it is energy in motion. Work is a process carried out by or on a system. In mechanical systems, work is defined as the action of a force on an item across a distance.

The term ‘work’ also refers to energy transfer and is related to thermodynamics. The gas performs work during expansion, and the gas performs work during compression. The job is dependent on the path and the initial and final states.

The system’s work is positive (+ve), while the system’s work is negative (-ve) (-ve). Let’s pretend a piston is filled with gas. The work is stated to be done by the gas and is positive when the piston rises upwards due to gas expansion. When the piston advances inward, the work done on the gas is considered negative.

Relation between Enthalpy and Internal Energy

Talking about the relationship between heat, work, and internal energy, here is a mathematical technique for proving that the internal energy of an ideal gas is exclusively a function of temperature and the rationale for the relationship between internal energy and enthalpy for an ideal gas.

An ideal gas’s internal energy (U) is calculated as follows:

U is equal to U(T)

The term enthalpy (H) is defined as follows:

H = U + PV ……(1)

where,

P stands for pressure, and

The volume of an ideal gas is V.

Let’s now apply the ideal gas equation to the previous equation, which is:

PV = RT

where,

R denotes the ideal gas constant, and

T refers to the temperature of an ideal gas.

⇒ H is equal to U + RT

The Enthalpy of an Ideal Gas is also written as:

H is equal to H(T)

Since the temperature-dependent specific heat at constant volume and pressure (Cv and Cp) is provided by:

dU is equal to Cv (T) dT

dH is equal to Cp (T) dT

The specific heat ratio k is calculated using the formulae above:

k = Cp / Cv=U / H

This is the relationship between heat, work, and internal energy for an ideal gas.

Conclusion

Thermodynamics is concerned with turning the quantity of thermal energy created by particle movement into mechanical energy. However, because thermodynamics deals with the bulk system rather than the body’s energy transformation or molecular constituents, it is essential to remember that it depends on the system’s beginning and end states. Thermodynamic rules deal with the energy changes that occur throughout a process. They have nothing to do with the speed with which the reaction occurs. We regularly use generic phrases like work, heat, and internal energy in thermodynamic terminology.