1 → 2 : isothermal compression. Because temperature is constant the internal energy of the gas does not change according to Eq.(2). According to Eq.(1) we also have\xa0p\xa0V\xa0=\xa0m\xa0R\xa0Tc=\xa0constant. This makes it possible to evaluate the work integral Wc\xa0=∫\xa0p\xa0dV This results in the equation : (8) Qc=Wc\xa0= m Rs\xa0Tc\xa0ln ( V1 / V2 )3 → 4 : isothermal expansion. This follows exactly the logic as the process 1 → 2. Hence, (9) Qh=Wh\xa0= m Rs\xa0Th\xa0ln ( V4 / V3 )2 → 3 : adiabatic compression. With κ = cp/cv\xa0for such process : (10) V2/V3\xa0= (Th/Tc)1/(κ-1)4 → 1 : adiabatic expansion. Follows the same logic as process 2 → 3 with the result: (11) V1/V4\xa0= (Th/Tc)1/(κ-1)\tWe use Eq.(8) and (9) to find a first expression for the efficiency of the Carnot cycle (see also Eq.(3) ) :(12) η = 1 - Qc/Qh\xa0= 1 - (Tc\xa0ln ( V1 / V2 )) / (Th\xa0ln ( V4 / V3 ))From Eq. (10) and (11) we get :(13) V1/V2\xa0= V4/V3and therefore :(14) η = 1 - Tc/Thi hope that you will like it

1.	I need Derivation on Carnot Cycle From Thermodynamics
Answer» For this questions you will need some mathematics and knowledge of engineering thermodynamics. Appropriate links are provided at the bottom of this section. As we saw previously all Carnot heat engine have the same efficiency irrespective of the working gas we are using. Hence, we might as well use an\xa0ideal gas\xa0with\xa0temperature-independent specific heats\xa0because its properties are precisely known and can be represented in terms of fairly easy equations. All noble gases ( helium, neon, argon, krypton, xenon, and the radioactive radon ) come extremely close to being an ideal gas at temperatures and pressure relevant to Stirling engine.(6) p V = m Rs\xa0T Ideal gas law(7) Δu = cv\xa0ΔT Change of internal energy is proportional to change in temperature\t		Figure 5 : Carnot Cycle
Show Answer