the final answer is not 553.52J and .453 Problem #3 Diatonic MPOSSIBLE HEAT ENGI

Question

the final answer is not 553.52J and .453

Problem #3 Diatonic MPOSSIBLE HEAT ENGINE (??) An inventor claims to have discovered a special "two-state" ideal gas that disociates into a monoatomic gas above (absolute pressure) P10.3psi but below that pressure stays diatomic. They further claim that it does so over a range of temperatures. The diatomic molecules are so weakly bound that you can ignore the binding energy (no internal energy change in going from the monoatomic to diatomic forms) You build an engine using the gas in the cycle shown, starting at room temperature 26 C at pressure #1 with 1 L of the gas in the diatom c state. The gas goes monoato pressure shoots up to 56psi at which point the engine undergoes a isothermal expansion until it gets back down to Pc as shown. c and the absolute The gas then condenses back down to diatomic, with the co-comittant pressure drop after which a lower temperature isotherm during compression returns the pressure to Pc (and the gas to point #I) (a) Compute the net work output of the engine per cycle. (b) Compute the ratio of the efficiency of the engine to the efficiency of a Carnot cycle running between T, andTe. What does this tell you about whether such an engine actually exists? JOAnswer part (a) ratio Answer part (b)

Explanation / Answer

work done in isothermal expansion = Wi = nRTln(Vf/Vi)

for isothermal expansion, n = 2n

Wi = 2nRTi*ln(Vf/Vi)

now, Initially

Pi = Pc = 10.3 Psi = 71016 Pa

Vi = 1 L = 0.001 m^3

Ti = PiVi/2nR = 4.27292418 /n

Ti = 26 + 273.16 = 299.16 K

hence

n = 0.014283073 mol

now at ppoint 2

P2 = 56 psi = 386106 Pa

V2 = V1

n2 = 2n

T2 = ?

T2 = P2V2/n2*R = 1626.49927 K

also

P3V3 = P2V2

P3 = 71016 Pa

V3 = 43.661869*V2 = 0.043661869 m^3

work doen in expansion Wi = 2n*R*1626.4992*ln(V3/V1) = 1458.1196462 J

after expansion,

P4V4 = nRT4

P3V3 = 2nRT3

V4 = V3

T4 = P4V3/nR = Ti

hence

Work absorbed = nRTi*ln(V1/V4) = -134.0950777 J

a. W0 = 1458.1196462 - 134.0950777 = 1324.0245 J/cycle

b. heat input is not known wo efificnency of this engine can be > 1

for carnot engine (Th - Tc)*100/Tc = 81.60712 %

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.