Thermodynamic Properties

We know from thermodynamics that heat is energy in transition. Therefore, heat has the same dimensions as energy and is measured in units of joule (J).

2.2.5 Specific Heat

The inherent thermal properties of a flowing gas become important when the Mach number is greater than 0.5. This is because Mach 0.5 corresponds to a speed of 650 km/h for air at sea level state, therefore

Подпись: du dT Подпись: v Подпись: (2.7)

for flow above Mach 0.5, the temperature change associated with velocity becomes considerable. Hence, the energy equation needs to be considered in the study and owing to this both thermal and calorical properties need to be accounted for in the analysis. The specific heat is one such quantity. The specific heat is defined as the amount of heat required to raise the temperature of a unit mass of a medium by one degree. The value of the specific heat depends on the type of process involved in raising the temperature of the unit mass. Usually constant volume process and constant pressure process are used for evaluating specific heat. The specific heats at constant volume and constant pressure processes, respectively, are designated by cv and cp. The definitions of these quantities are the following:

Подпись: cp — Подпись: dh  dT ) p Подпись: (2.8)

where u is internal energy per unit mass of the fluid, which is a measure of the potential and more particularly the kinetic energy of the molecules comprising the gas. The specific heat cv is a measure of the energy-carrying capacity of the gas molecules. For dry air at normal temperature, cv =717.5 J/(kg K). The specific heat at constant pressure is defined as:

where h = u + pv, the sum of internal energy and flow energy is known as the enthalpy or total heat constant per unit mass of fluid. The specific heat at constant pressure cp is a measure of the ability of the gas to do external work in addition to possessing internal energy. Therefore, cp is always greater than cv. For dry air at normal temperature, cp = 1004.5 J/(kg K).

Note: It is essential to understand what is meant by normal temperature. For gases, up to certain temper­ature, the specific heats will be constant and independent of temperature. Up to this temperature the gas is termed perfect, implying that cp, cv and their ratio у are constants, and independent of temperature. But for temperatures above this limiting value, cp, cv will become functions of T, and the gas will cease to be perfect. For instance, air will behave as perfect gas up to 500 K. The temperature below this liming level is referred to as normal temperature.

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