The Ideal Gas Law relates pressure, volume, molecular quantity, and temperature of an ideal gas
together in one neat mathematical expression:
PV = nRT
Where,
P = Absolute pressure (atmospheres)
V = Volume (liters)
n = Gas quantity (moles)
R = Universal gas constant (0.0821 L · atm / mol · K)
T = Absolute temperature (K)
An alternative form of the Ideal Gas Law uses the number of actual gas molecules (N) instead
of the number of moles of molecules (n):
PV = NkT
Where,
P = Absolute pressure (atmospheres)
V = Volume (liters)
N = Gas quantity (moles)
k = Boltzmann’s constant (1.38 × 10−23 J / K)
T = Absolute temperature (K)
Although no gas in real life is ideal, the Ideal Gas Law is a close approximation for conditions of
modest gas density, and no phase changes (gas turning into liquid or visa-versa).
Since the molecular quantity of an enclosed gas is constant, and the universal gas constant must
be constant, the Ideal Gas Law may be written as a proportionality instead of an equation:
PV ∝ T
Several “gas laws” are derived from this Ideal Gas Law. They are as follows:
PV = Constant Boyle’s Law (assuming constant temperature T)
V ∝ T Charles’s Law (assuming constant pressure P)
P ∝ T Gay-Lussac’s Law (assuming constant volume V )
You will see these laws referenced in explanations where the specified quantity is constant (or
very nearly constant).
For non-ideal conditions, the “Real” Gas Law formula incorporates a corrected term for the
compressibility of the gas:
PV = ZnRT
Where,
P = Absolute pressure (atmospheres)
V = Volume (liters)
Z = Gas compressibility factor (unitless)
n = Gas quantity (moles)
R = Universal gas constant (0.0821 L · atm / mol · K)
T = Absolute temperature (K)
The compressibility factor for an ideal gas is unity (Z = 1), making the Ideal Gas Law a limiting
case of the Real Gas Law. Real gases have compressibility factors less than unity (< 1). What this
means is real gases tend to compress more than the Ideal Gas Law would predict (i.e. occupies less
volume for a given amount of pressure than predicted, and/or exerts less pressure for a given volume
than predicted).
Friday, March 23, 2012
FLUID MECHANICS | Gas Laws
Sunday, March 18, 2012
The Thermodynamic Laws
The laws of thermodynamics explain the effects of heat in an engine. The first law states that energy can be changed but it cannot be destroyed. In a gas turbine engine, heat energy is changed to mechanical energy. The second law of thermodynamics states that heat cannot be transferred from a cooler body to a hotter body. In a gas turbine engine, heat is transferred from the hotter engine to the cooler lube oil.
Newton's first law explains why a force is needed to make the gas turbine work. In the figure, a ball on a level table will not move until it is made to move by some force such as the wind or pushing it by hand. Similarly, until the fuel and air mixture is burned in the gas turbine, there is no force for the turbine to use to turn the rotor shaft.
Newton's Second Law explains why the air must be compressed and accelerated to create a force. In the figure, a hammer is used to drive a nail. The force of hitting the nail is proportional to the mass (weight) of the hammer multiplied by the velocity of the hammer when it hits the nail. If you also use a heavier hammer, it is even easier to drive the nail into the wood. Mass and acceleration directly affect the amount of force created. The more compressed air (mass) that enters the gas turbine, the more force created from the combustion process.
