2) The first law states that the energy of the universe is a constant (AU = q + w) while the second law states that the entropy of the universe tends always towards a maximum (AStot = AS + ASurr 20). Answer the following questions only based on the conditions it is provided. (a) Assuming that the entropy change of the system is AS = qrey/T ,determine the relationship of Assurr in terms of qrev and T. (b) If only PV-work is considered, prove that the inequality of work (dwrev< dwir) is always valid (e.g., expansion or compression). (c) Prove dqrev> dqirr based on dwrev< dwirr.

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2) The first law states that the energy of the universe is a constant (AU = q + w) while the
second law states that the entropy of the universe tends always towards a maximum (AStot =
AS + ASsurr 20). Answer the following questions only based on the conditions it is provided.
(a) Assuming that the entropy change of the system is AS = qrey/T ,determine the relationship
of Asşurr in terms of qrev and T.
(b) If only PV-work is considered, prove that the inequality of work (dwrev< dwir) is always
valid (e.g., expansion or compression).
(c) Prove dgrev> dqirr based on dwrev < dwir.
(d) Based on dqrev > dqir to prove the Clausius inequality, dS > qrev/T , where the equality
holds only for reversible processes.
(e) Following (c) and (d) to prove that the entropy change of any irreversible process is
always greater than zero in an isolated system.
(f) Assuming that the system is no longer isolated, i.e., the surroundings are a reservoir of
energy and the heat entering the system is equal to the heat leaving the surroundings. Show
that the Clausius inequality can be deduced to a more general expression for the 2nd law, i.e.,
dS = dS + dSgurr 20
'tot
Transcribed Image Text:2) The first law states that the energy of the universe is a constant (AU = q + w) while the second law states that the entropy of the universe tends always towards a maximum (AStot = AS + ASsurr 20). Answer the following questions only based on the conditions it is provided. (a) Assuming that the entropy change of the system is AS = qrey/T ,determine the relationship of Asşurr in terms of qrev and T. (b) If only PV-work is considered, prove that the inequality of work (dwrev< dwir) is always valid (e.g., expansion or compression). (c) Prove dgrev> dqirr based on dwrev < dwir. (d) Based on dqrev > dqir to prove the Clausius inequality, dS > qrev/T , where the equality holds only for reversible processes. (e) Following (c) and (d) to prove that the entropy change of any irreversible process is always greater than zero in an isolated system. (f) Assuming that the system is no longer isolated, i.e., the surroundings are a reservoir of energy and the heat entering the system is equal to the heat leaving the surroundings. Show that the Clausius inequality can be deduced to a more general expression for the 2nd law, i.e., dS = dS + dSgurr 20 'tot
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