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Unformatted text preview: 3. The Second Law Motivation of the Second Law : In the following table, the first column shows a particular state A of the sys tem, as defined by its temperature, volume and com position, and the second column shows another state B, characterized by different values of some or all of these variables. Table 1 (All systems are in an adiabatic enclosure) State A State B Two equal blocks of cop per are connected by a wire. One block is at 20 ◦ C and the other at 30 ◦ C . The blocks are each at 25 ◦ C . A dilute gas at a tem perature T occupies one half of a vessel and the other half is vacuum. The gas at the same temperature T occupies the whole of the vessel 1 K. Denbigh: The Principles of Chemical Equilibrium (Cambridge UP, Cam bridge 1966) PChem I 3.1 A dilute gas X occupies one half of a vessel and a dilute gas Y occupies the other half. The tem perature is T . The gases are uniformly mixed in the vessel and the temperature has the same value T . A vessel contains hydro gen and oxygen and a catalyst. The volume is V and the temperature is T . The vessel contains the same amount of hydro gen and oxygen, com bined as water, togeth er with the catalyst. The volume is V and the temperature exceeds T by an amount corre sponding to the heat of reaction. Question: Are the processes A→ B and B→ A al lowed? Answer: Energy is conserved for all A→ B and B→ A processes. The processes are allowed by the First Law. PChem I 3.2 Question: Are the processes A→ B and B→ A ob served? Answer: Only the processes A→ B are observed to occur. =⇒ spontaneous direction Spontaneity or nonspontaneity of the processes A→ B and B→ A depends entirely on the nature of the states A and B. =⇒ We expect that there exists a state function, S , that characterizes the spontaneous direction of a pro cess. Second Law of Thermodynamics : Heat flows sponta neously from a hot object to a cold object. Equivalent form: No process is possible in which the sole result is the absorption of heat from a reservoir and its com plete conversion into work. need mathematical form parallel to First Law PChem I 3.3 First Law (permissible change) 1) There exists a state function U 2) d U = d q + d w Second Law (spontaneous change) ( 1 ) There exists a state function S , the entropy , for the system. ( 2 ) If the state of the system changes, then d S = d q rev T derive the mathematical form consider a classical ideal gas, n = const First Law: d U = d q rev + d w rev = d q rev P d V , reversible change, no extra work Joule experiment: d U = C V d T C V d T = d q rev P d V PChem I 3.4 d q rev = C V d T + P d V ∂ q rev ∂ T ¶ V = C V , ∂ q rev ∂ V ¶ T = P are mixed second derivatives equal?...
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 Spring '08
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 Thermodynamics, Entropy, tc

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