Page 28 - Aerodynamics for Engineering Students

Basic concepts and definitions 11

1.2.8 Thermodynamic properties
Heat, like work, is a form of energy transfer. Consequently, it has the same dimen-
sions as energy, i.e. ML2T-2, and is measured in units of Joules (J).

Specific heat
The specific heat of a material is the amount of heat necessary to raise the tempera-
ture of unit mass of the material by one degree. Thus it has the dimensions L2T-26-'
and is measured in units of J kg-' "C-' or J kg-' K-'.
With a gas there are two distinct ways in which the heating operation may be
performed: at constant volume and at constant pressure; and in turn these define
important thermodynamic properties.
Specific heat at constant volume If unit mass of the gas is enclosed in a cylinder
sealed by a piston, and the piston is locked in position, the volume of the gas cannot
change, and any heat added is used solely to raise the temperature of the gas, i.e. the
head added goes to increase the internal energy of the gas. It is assumed that the
cylinder and piston do not receive any of the heat. The specific heat of the gas under
these conditions is the specific heat at constant volume, cy. For dry air at normal
aerodynamic temperatures, cy = 718 J kg-' K-'.
Internal energy (E) is a measure of the kinetic energy of the molecules comprising
the gas. Thus
internal energy per unit mass E = cvT

or, more generally,
cv= [%Ip

Specific heat at constant pressure Assume that the piston referred to above is now
freed and acted on by a constant force. The pressure of the gas is that necessary to
resist the force and is therefore constant. The application of heat to the gas causes its
temperature to rise, which leads to an increase in the volume of the gas, in order to
maintain the constant pressure. Thus the gas does mechanical work against the force.
It is therefore necessary to supply the heat required to increase the temperature of the
gas (as in the case at constant volume) and in addition the amount of heat equivalent
to the mechanical work done against the force. This total amount of heat is called the
specific heat at constant pressure, cp, and is defined as that amount of heat required
to raise the temperature of unit mass of the gas by one degree, the pressure of the gas
being kept constant while heating. Therefore, cp is always greater than cy. For dry air
at normal aerodynamic temperatures, cp = 1005 J kg-' K-' .
Now the sum of the internal energy and pressure energy is known as the enthalpy
(h per unit mass) (see below). Thus

h = cpT

or, more generally,
cP= [g]

P