An ideal gas undergoes the cycle shown in the figure below: it expands isobarically at pressure p from volume V to volume XV, cools isometrically, and then returns isothermally to its initial state. þ i 3 → 1 isothermal 2 XV 3 V a) Derive the following expressions for the heat flowing in or out of the system in terms of X, pand V. 1 → 2 Q12 = PV(x - 1) 2→ 3 Q23 =pV (1- Q31 = -pV log › b) Hence derive that the efficiency is e= (1-101). log R
An ideal gas undergoes the cycle shown in the figure below: it expands isobarically at pressure p from volume V to volume XV, cools isometrically, and then returns isothermally to its initial state. þ i 3 → 1 isothermal 2 XV 3 V a) Derive the following expressions for the heat flowing in or out of the system in terms of X, pand V. 1 → 2 Q12 = PV(x - 1) 2→ 3 Q23 =pV (1- Q31 = -pV log › b) Hence derive that the efficiency is e= (1-101). log R
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
Transcribed Image Text:An ideal gas undergoes the cycle shown in the figure below: it expands isobarically at pressure p from volume V to volume XV, cools
isometrically, and then returns isothermally to its initial state.
2→ 3
i
3 →→ 1
V
XV
a) Derive the following expressions for the heat flowing in or out of the system in terms of X, p and V.
1 → 2
Q12 = PV(x - 1)
Q23 = CPV (1-X)
isothermal
Q31
=
3
-pV log X
R
log
b) Hence derive that the efficiency is e= (1 - 101)
X-1
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