Jamil Ghojel - Fundamentals of Heat Engines

If a gas mixture of two components A and B is at pressure p and temperature T in a container with volume V , each gas in the mixture exists separately and independently at the temperature and volume of the mixture, and their respective pressures are p Aand p B. For the mixture

For the components,

Since n = n A+ n B,

or

(1.45)

p Aand p Bare known as the partial pressures .

Therefore,

It can be shown that the internal energy and enthalpy of a mixture of two gases (A and B) can be written as

The gas constants for the i th component and gas mixture are, respectively,

Using Eq. (1.43), we obtain

(1.46)

For the two‐gas mixture

The state of a gas may be completely specified by combining three variable properties (pressure p , temperature T , and volume V ) in an equation called the ideal gas equation of state :

(1.47)

The terms in Eq. 1.47are as follows:

Pressure p is in N/m2 or Pa.

Volume V is in m3.

Mass m is in kg.

Temperature T is in K.

Specific volume v is in m3/kg.

Molar amount of gas n is in kmole (1 kmole of any gaseous substance occupies a volume of 22.41 m3 at the standard temperature 0°C and pressure 101.325 Pa).

Gas constant in J/kg. K.

Molecular mass of any gas μ is in kg/kmole.

Universal gas constant

An adiabatic process is one where the energy of the system changes only by means of work transfer, and there is no heat crossing the boundary. The relationship between the state properties can be written as

(1.48)

The volume V can be replaced by the specific volume v = V / m , which yields the additional equation p 1/ p 2= ( v 2/ v 1) γ. The exponent γ is the ratio of specific heat capacities. The specific heat capacity (the word capacity will be dropped in future references) is defined as the amount of heat energy required to raise the temperature of a unit quantity of matter by one degree Celsius (on a mass basis c in J / kg . K and on a mole basis C in J / kmole . K ). The specific heat at constant pressure is written as c pin J / kg . K or C pin J / kmole . K and at constant volume as c vin J / kg . K or C vin J / kmole . K . Both c pand c vincrease with temperature. Table A.1 in Appendix A shows the molar specific heats at constant pressure of some gases as a function of temperature. The specific heat at constant volume can be determined from the following equations, assuming the gases behave as ideal gases:

A hot object tends to cool to the temperature of colder surroundings, and a cold object is warmed to the temperature of hotter surroundings. The phenomenon is caused by the heat‐transfer process, in which the energy of a system changes while no work is done on or by the system (no work exchange with the surroundings). This process can occur with the volume remaining constant, and the change of energy in the system for an ideal gas is then

(1.49)

ΔU is the internal energy of the system.

If the pressure remains constant during the process, the change of energy in the system is

(1.50)

The source of the heat in both these cases could be external or internal. Examples of processes with internal heat sources are the spark ignition engine (constant‐volume combustion of the fuel) and the gas turbine combustor (constant‐pressure combustion of the fuel).