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Expansion of an ideal gas. An ideal gas sample contains n moles, initially has a volume Vi and a temperature Ti , and at the end of the expansion has a volume Vf > Vi . We will study three processes. Process I is an adiabatic expansion against vacuum: the gas initially is contained in one part of an insulated container, with the other part being empty, and the partition separating the two parts is suddenly removed, allowing the gas to expand against zero pressure. Process II is a reversible isothermal expansion. Process III is a reversible adiabatic expansion. For each of the three processes, determine the heat Q absorbed by the gas, the work W done on the gas, and the changes ∆E, ∆T and ∆S in the energy, temperature and entropy. Write all results in terms of n, R, Vi , Vf , and Ti . Compare the results for the three processes, and indicate which quantities are the same for each pair of processes (I and II; II and III; I and III), or what is the direction of their inequality if they are different, justifying those equalities and inequalities in terms of basic physical concepts.

Expansion of an ideal gas. An ideal gas sample contains n moles, initially has a volume Vi and a temperature Ti , and at the end of the expansion has a volume Vf > Vi . We will study three processes. Process I is an adiabatic expansion against vacuum: the gas initially is contained in one part of an insulated container, with the other part being empty, and the partition separating the two parts is suddenly removed, allowing the gas to expand against zero pressure. Process II is a reversible isothermal expansion. Process III is a reversible adiabatic expansion. For each of the three processes, determine the heat Q absorbed by the gas, the work W done on the gas, and the changes ∆E, ∆T and ∆S in the energy, temperature and entropy. Write all results in terms of n, R, Vi , Vf , and Ti . Compare the results for the three processes, and indicate which quantities are the same for each pair of processes (I and II; II and III; I and III), or what is the direction of their inequality if they are different, justifying those equalities and inequalities in terms of basic physical concepts.

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Expansion of an ideal gas. An ideal gas sample contains n moles, initially has a volume Vi
and a temperature Ti
, and at the end of the expansion has a volume Vf > Vi
. We will study three
processes. Process I is an adiabatic expansion against vacuum: the gas initially is contained in one part
of an insulated container, with the other part being empty, and the partition separating the two parts is
suddenly removed, allowing the gas to expand against zero pressure. Process II is a reversible isothermal
expansion. Process III is a reversible adiabatic expansion. For each of the three processes, determine the
heat Q absorbed by the gas, the work W done on the gas, and the changes ∆E, ∆T and ∆S in the energy,
temperature and entropy. Write all results in terms of n, R, Vi
, Vf , and Ti
. Compare the results for the
three processes, and indicate which quantities are the same for each pair of processes (I and II; II and III;
I and III), or what is the direction of their inequality if they are different, justifying those equalities and
inequalities in terms of basic physical concepts. 

Ideal gas. Consider an ideal gas, i.e. a gas that satisfies the following three conditions: i) pV = nRT, JE ii) ᎧᏙ = 0, and n,T iii) for a reversible adiabatic process pV=const with y = cp/cv. Assume that y is temperature independent.
Transcribed Image Text:Ideal gas. Consider an ideal gas, i.e. a gas that satisfies the following three conditions: i) pV = nRT, JE ii) ᎧᏙ = 0, and n,T iii) for a reversible adiabatic process pV=const with y = cp/cv. Assume that y is temperature independent.
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