High Enthalpy Gas Dynamics
High Enthalpy Gas Dynamics
High-enthalpy flows are those with their specific heats ratio as a function of temperature. The word enthalpy is based on the Greek word enthalpies, which means to put heat into. It comes from the classical Greek prefix en-, meaning to put into, and the verb thalpein, meaning "to heat." The earliest writings to contain the concept of enthalpy did not appear until 1875 when Josiah Willard Gibbs introduced "a heat function for constant pressure" . However, Gibbs did not use the word "enthalpy" in his writings. Instead, the word "enthalpy" first appeared in the scientific literature in a 1909 publication by J. P. Dalton. According to that publication, Heike Kamerlingh Onnes (1853-1926) actually coined the word. Over the years, many different symbols were used to denote enthalpy . It was not until 1922 that Alfred W. Porter proposed the symbol "" as the accepted standard , thus finalizing the terminology still in use today.
Enthalpy is a measure of the total energy of a thermodynamic system. It includes the internal energy, which is the energy required to create a system, and the amount of energy required to make room for it by displacing its environment and establishing its volume and pressure.
Enthalpy is a thermodynamic potential. It is a state function and an extensive quantity. The unit of measurement for enthalpy in the International System of Units (SI) is the joule, but other historical, conventional units are still in use, such as the British thermal unit and the calorie.
The enthalpy is the preferred expression of system energy changes in many chemical, biological, and physical measurements, because it simplifies certain descriptions of energy transfer. This is because a change in enthalpy takes account of energy transferred to the environment through the expansion of the system under study.
The total enthalpy, , of a system cannot be measured directly. Thus, change in enthalpy, , is a more useful quantity than its absolute value. The change is positive in endothermic reactions and negative in heat-releasing exothermic processes. of a system is equal to the sum of nonmechanical work done on it and the heat supplied to it.
The enthalpy, , of a homogeneous system is defined as
where , , and , respectively, are the internal energy, pressure, and volume of the system.
The enthalpy is an extensive property . This means that for a homogeneous system, the enthalpy is proportional to the size of the system. It is convenient to work with the specific enthalpy , where is the mass of the system, or the molar enthalpy , where is the number of moles ( and are intensive properties ) while working with practical problems. For an inhomogeneous system, the enthalpy is the sum of the enthalpies of the subsystems composing the system.
where the label refers to the various subsystems. In a system with continuously varying , , and/or composition, the summation becomes an integral:
where is the density.
The enthalpy of a homogeneous system can be derived as a characteristic function of the entropy and the pressure as follows.
Let us start from the first law of thermodynamics for a closed system
Here, is a small amount of heat added to the system and is a small amount of work performed by the system. In a homogeneous system, only reversible processes can take place, so the second law of thermodynamics gives
where is the absolute temperature of the system and is the entropy. Furthermore, if only work is done, . For this case, from first law of thermodynamics
Adding to both sides, we have
This can be expressed as
The expression of in terms of entropy and pressure may be unfamiliar to many readers. However, there a