Week 3 (Thermodynamic Properties ll - Ideal Gases) Flashcards
Thermodynamic Properties ll - Ideal Gases
The ideal gas law is an example of an …
equation of state
The development of a mathematical model based purely on…
empirical evidence, i.e. the results of experiments.
Robert Boyle worked out…
At constant temperature, as Pressure increases, Volume decreases by the same
proportion implying the product, PV, is constant.
PV = constant
(boyle’s law)
In the equation PV = constant or V /T = constant, is the value of the constant the same for all gases
the constant is different for different gases
Jacques Charles and Joseph Louis Gay-Lussac worked out…
At constant Pressure, as Thermodynamic Temperature increases, Volume increases by
the same proportion implying that the ratio, V/T is constant.
V/T = Constant
(Charle’s law)
Joseph Louis Gay-Lussac worked out…
At constant Volume, as Temperature increases, Pressure increases by the same
proportion implying that the ratio, P/T is constant.
P/T = Constant
(s Gay-Lussac’s Law)
Combine the three Laws, along with Avogadro’s Law (states that under the same conditions of temperature and pressure, equal volumes of different gases contain an equal number of molecules), to arrive at the ideal gas law:
P v = R T
T is Absolute Temperature (kelvin)
v, specific vol
R, the specific ideal gas constant, a constant particular to the fluid under consideration
How can we calc R
R = R sub(u) / M
R sub(u) is the same as R with ~ on top
R sub(u) = the Universal Gas Constant, equal to 8.31447 kJ/kmol K
M, molar mass of the substance,
i.e. the mass in grams of one mole of the substance.
Approximate values of M are, for example, Carbon dioxide (CO2), 44, Oxygen (O2), 32,Nitrogen (N2) 28.
More accurate values for these and other gasses are given in Rogers and Mayhew.
If we multiply both sides of the ideal gas law by the mass, m, of a sample of ideal gas, we obtain:
P V = m R T
An ideal gas is an imaginary substance which obeys the above relations exactly.
The ideal gas equation
has been shown to give good results over a wide range of conditions, provided that:
a) The temperature is not too low
b) The pressure is not too high (by not too high we mean well below the critical
pressure of the substance.)
Kinetic Theory of Gases
model the behaviour of gases from a
more fundamental standpoint by making assumptions about the behaviour of individual molecules in the gas and seeing what results these yield for the variation of Macroscopic properties such as pressure and temperature.
Assumptions of the Kinetic Theory of Gases (6)
1 The average distance separating the gas particles (ie their mean-free path length
between collisions) is large compared to their size.
2 The particles have the same mass.
3 The number of particles is so large that statistical treatment can be applied.
4 The particles are in constant, random, and rapid motion.
5 Except during collisions, the interactions among particles are negligible.
6 The average kinetic energy of the gas particles depends only on the absolute
temperature of the system.
At high pressure, where the original ideal gas equation breaks down, we can note that assumption 1 above will be violated as at high pressures the particles will be “squashed” closer and closer together.
At low temperature again where the original ideal gas equation breaks down, the
molecules are moving more slowly and are therefore near one another for longer time periods and are able to interact due to attractive force between them, therefore assumption 5 above will be violated.
Compressibility factor – a correction to the ideal gas law
We can add an empirical correction to the ideal gas law by defining a “compressibility
factor”, Z, as follows:
Z = Pv / RT = v sub(actual) / v sub(ideal)
Equation for reduced pressure and reduced temperature:
P sub(R) = P / P sub(critical)
‘’ ‘’
The principle of corresponding states.
On the graph of Z against reduced pressure and reduced temp along the curved lines the data for all the different types of fluids (e.g water and CO2) fall on the same lines, indicating that Z is the same for all fluids at the same T sub(R) and P sub(R)
.
