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Lecture note


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  • 2. Outline
    The need for the second law
    Concept of entropy
    Statements of the second law
    Properties of entropy
    Derivation of equation for entropy
    Consequences of the second law
  • 3. Introduction
    The second law explains the phenomenon of irreversibility in nature
    The need for the second law arises because the first law failed in some aspects. For example,
    It fails to explain why natural processes have a preferred direction
    The first law fails to produce thermodynamic functions that can be used to predict the direction of a spontaneous reaction
    The second law deals with entropy
  • 4. Entropy
    The key concept for the explanation of phenomenon through the second law is the definition of a physical property called entropy
    Entropy is a measure of the degree of disorderliness of a system.
    A change in entropy of a system is the infinitesimal transfer of heat to a close system driving a reversible process divided by the equilibrium temperature (T) of the system, i.edS = dqrev /T
  • 5. Statements of the second law
    No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature (Clausius-Mussoti)
    No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work (Kelvin-Plank)
    Equivalent ways of stating the laws are
    i. the entropy of a spontaneous reaction increases and tends toward a maximum
    ii. After any spontaneous reaction, work must be converted to heat in order to restore the system to its initial state
  • 6. Properties of entropy
    Entropy is a state function: its properties depends on the initial and final state of the system
    Entropy is additive. i.e ST = S1 + S2 + S3 + -----
    Entropy is a probability function
  • 7. Derivation of expression for entropy change
    If the probability of finding a system in state 1 and 2 are W1 and W2, then the probability of finding the system in the two parts is the total probability, W = W1 x W2,
    S(W) = S(W1) x S(W2) = S(W1) + S(W2) (1)
    Conditions set by Eq 1 can only be fulfilled if entropy is logarithm dependent, i.e
    S = log(W1 x W2) = logW1 x logW2 (2)
    Consider an ideal gas expanding into two systems joined together, the probabilities for the first and second is proportional to their respective volumes, therefore, W1 = aV1, W2 = aV2 and since S is additive, S = S2 – S1 = log(aV2) – log(aV1) = log(V2/V1)
    From first law of thermodynamics, it can be shown that the reversible work done = reversible heat absorbed = nRTln(V2/V1) and if we multiply S by the constants, 2.303R, we have, qads = T x S. It therefore follows that S can be expressed as follows
    S = qads/T (3)
  • 8. Consequence of the second law of thermodynamics
    We shall consider the following consequences of the 2nd law of thermodynamics,
    Entropy change for an ideal gas
    Entropy of mixing ideal gases
    Carnot cycle
    Free energy change
  • 9. Entropy change for an ideal gas
  • 10. Entropy of mixing ideal gases
  • 11. Reversible cycle and efficiency: Carnot cycle
  • 12. Free energy
  • 13. Effect of pressure and temperature
  • 14. S and spontaneousity of a reaction
    When S is positive, spontaneous reaction
    When S is zero, reaction at equilibrium
    When S is negative, non spontaneous
    Limitation is that we who measures the entropy are part of the environment. Therefore S is not a unique parameter for predicting the direction of a chemical reaction
  • 15. G and spontaneousity of a reaction
    G > 0, non spontaneous (H > TS)
    G < 0, spontaneous (H < TS)
    G = 0, reaction at equilibrium (H = TS
    G is a state function obtained at constant pressure. At constant volume the state function is work function expressed as
    A = E - TS
    When A > 0, spontaneous
    When A <0 , non spontaneous
    When A = 0, at equilibrium
    Thermodynamic function obtained from the second law is entropy
    Entropy is a measure of disorderliness while enthalpy measures orderliness
    Entropy data must be combined with enthalpy (or internal energy data) in order to predict the direction of a chemical reaction