Heat

What is Heat in Thermodynamics?

Imagine you’re holding a warm cup of coffee on a chilly morning. The warmth you feel isn’t just the temperature; it’s heat, energy transferred from the hot liquid to your hand. In thermodynamics, heat is defined as the transfer of energy between systems through modes other than work and matter exchange.

The Measurement of Heat

In the realm of science, measuring heat isn’t just about feeling warmth; it’s quantifying that energy. The joule (J) is the standard unit used in the International System of Units to measure heat. But for practical applications, engineers and scientists often use other units like the British thermal unit (BTU) or calorie.

The Concept of Calorimetry

Calorimetry, a method that measures the amount of energy transferred as heat by its effect on interacting bodies, is crucial in understanding how heat works. The symbol Q for heat was introduced way back in 1859, marking an important milestone in thermodynamics.

The Nature of Heat Transfer Rate

Heat transfer rate or the flow per unit time is denoted by Q˙. However, it’s not a function of state and cannot be written with the dot notation as a derivative of a function. This concept is pivotal in understanding how heat moves through different materials.

The Historical Evolution of Heat Theory

In ancient times, people thought of ‘heat’ as a separate form of matter. Galileo suspected that it was an artifact of our minds, while Robert Hooke and Robert Boyle reiterated the particle motion theory. John Locke wrote about heat as a brisk agitation of insensible parts producing sensation.

The 18th Century: A Turning Point in Heat Theory

During the 18th century, the concept of ‘heat’ began to take shape. Brook Taylor measured temperature changes in mixtures of hot water, while William Cullen experimented with diethyl ether. Benjamin Franklin and John Hadley found that as the ether evaporated, the temperature decreased.

The Discovery of Specific Heat

Joseph Black conducted extensive studies on heat, introducing the concept of specific heat capacity in 1760. He demonstrated an experiment where he mixed water and mercury at different temperatures to show that they change temperature differently when combined.

The Measurement of Degrees of Heat

Black used a unit called ‘degrees of heat’ instead of just ‘degrees.’ This was context-dependent, based on the mass of substances involved. He showed that if equal masses of ice and water were mixed, the heat gained by the water and lost by the mercury would be the same.

The 19th Century: Defining Heat

In the 1850s, Rudolf Clausius introduced the process function Q, describing it as ‘amount of heat.’ James Clerk Maxwell outlined four stipulations for defining heat in his 1871 work. He stated that heat can be transferred from one body to another, is a measurable quantity, and cannot be treated as a material substance.

The Carathéodory Approach

Carathéodory’s definition of heat in 1909 was based on processes in a closed system. He defined the quantity of heat transferred (Q) as the change in internal energy minus the amount of work done by the body on its surroundings, Q = ΔUY – W.

The Mechanical View of Thermodynamics

According to this view, quantity of energy transferred as heat is a derived concept defined for closed systems. A calorimeter measures changes in a body’s properties due to heat transfer, relying on hypothetical quantities and the first law of thermodynamics.

The Transfer of Heat: Conduction, Radiation, and Convection

Heat can be transferred through conduction (from a hot body to a cold one), radiation (a hotter body losing heat to a colder one without an intervening medium becoming hot), or convection (transport of internal energy). These processes are fundamental in understanding how thermal energy moves from one place to another.

The Role of Heat Engines and Refrigerators

Heat engines and refrigerators operate on the principle that heat can be transferred between two bodies. A heat engine transfers heat from a hot reservoir to a cold one, while a refrigerator does the opposite. Both processes involve work being done by an external source.

The Three Main Conceptual Approaches to Heat

Planck identified three main approaches: microscopic (kinetic theory), macroscopic (mechanical view), and statistical mechanics. The mechanical view regards quantity of energy transferred as heat as a derived concept, defined for closed systems.

The Definition of Heat in Thermodynamics

Heat transfer is described through the first law of thermodynamics: ΔU = Q – W. Here, Q represents the quantity of heat added to an object, and W is the work done by the system on its surroundings.

The Significance of Entropy in Thermodynamics

Entropy, a measure of disorder or randomness, plays a crucial role in thermodynamics. The second law states that if heat is supplied to a system in a reversible process, the increment of heat and temperature form an exact differential: dS = δQ / T.

The Fundamental Thermodynamic Relations

These relations include U = U(S,V) for internal energy, H = U + PV for enthalpy, and the fundamental thermodynamic relation: U = U(S,V). For a process at constant pressure, ΔH = Q – PΔV.

The Conclusion

Understanding heat in thermodynamics is not just about measuring temperature; it’s about grasping how energy transfers between systems. From the ancient theories of heat as a separate form of matter to modern definitions based on entropy and state functions, the journey through thermodynamics reveals the intricate nature of thermal energy transfer.