MATLS 2B03 Lecture Notes - Lecture 14: Thermodynamics, Electrolysed Water, Ideal Gas
29 Aug 2016
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Chapter 4, 8,15(15.1 – 15.3)
1. Chapter 4 – The Statistical Interpretation of Entropy
• “ -up-” atomic or molecular level. It
means that the more mixed up the constituent particles of a system, the larger the value of its entropy.
• The entropy of the gaseous state is greatest than that of the liquid state and the entropy of the liquid state is greater than that of the
solid state.
• The transformation of a solid to a liquid at its melting temperature, Tm, requires that the substance absorb a quantity of heat, q, called
the LATENT HEAT OF MELTING. The entropy of the substance being melted is thus increased by the amount q/Tm and, if the melting
is done at constant pressure then q = H.
• The equilibrium melting or freezing temperature of a substance can thus be defined as that temperature at which no change in the
degree of order of the combined system (Substance + Heat Reservoir) occurs as a result of the phase change. Only at this temperature
are the solid and liquid in equilibrium with one another, and hence, only at this temperature can the phase change occur reversibly.
Microstates
✓ The equilibrium state of a system is simply the most probable of all of its possible states, and the subject is concerned with
determination of, the criteria governing, and the properties of this most probable state.
✓ If a particle is confined to move within a given fixed volume, then the particle may only have certain discrete allowed valued of
energy, which are separated by th “ ”.
levels decreases as the volume available to the movement of the particle increases, and energy becomes continuous only when
no restriction is placed on the position of the particle.
✓ Microstates are just distinguishable arrangements in which the particles can reach a certain total energy of the system through
placement in different energy levels in order to reach the total energy of the system, U.
✓ A single macrostate is made up of the total number of microstates that the particle can reach in order to reach its total energy of
its system. It is fixed when the values of the independent variable are fixed.
✓ The macrostate of the system is determined by the fixed values of U, V and number of particles.
✓ The distribution of particles in the energy levels which maximizes the most probable distribution is this one in which the
occupancy of the levels decreases exponentially with increasing energy.
✓ Stirling Approximation: ln X! = X*ln(X) – X
• An increase in temperature causes the upper energy levels to become more relatively more populated, and this corresponds to an
increase in the average energy of the particles.
• S = k ln(): It is called the
Bza’ ai
which shows the required quantitative relationship between the entropy of a
’ “ -up-”, , , is the number of ways in which the energy of the system
can be distributed among the particles. The Boltzmann equation shows that an increase in the number of microstates made available
to the system causes an increase in the entropy of the system.
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2
• The most probable state of the system is that in which has a maximum value, consistent with the fixed values of U, V and n, and
hence the equilibrium state of the system is that in which S is a maximum, consistent with the fixed values of U, V and n.
• Classical Thermodynamics shows that the transfer of heat from a body at some temperature to a body at a lower temperature is an
irreversible process which is accompanied by the production of entropy.
• The total entropy of a system is the sum of the thermal entropy, Sth, and the configurational entropy, Sco and the total number of
microstates available to the system is the product thconf.
2. Chapter 8 – The Behavior Of Gases
• PV = RT, is the equation of an ideal gas and is called the Ideal Gas Law. A gas which obeys this law over a range of states is said to
behave ideally in this range of states, a gas which obeys this law in all states is called a perfect gas.
• Several features of the figure should be noted. First, there is a region in which liquid and vapor can coexist, bounded by the liquid
saturation curve on the left and the vapor saturation curve on the right. This is roughly dome-shaped and is thus often referred to as
the ``vapor dome.'' Outside of this regime, the equilibrium state will be a single phase. The regions of the diagram in which the system
will be in the liquid and vapor phases respectively are indicated. Second is the steepness of the isotherms in the liquid phase, due to
the small compressibility of most liquids. Third, the behavior of isotherms at temperatures below the ``critical point'' in the region to
the right of the vapor dome approach those of an ideal gas as the pressure decreases, and the ideal gas relation is a good
approximation in this region.
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