Question

6) In a reversible Carnot heat engine which operates between reservoirs at Thigh 500 K and Tlow = 300 K with a net power output of 600 W, methane gas is used as working fluid. Methane can be considered here as an ideal gas with M 16.043 g mol-, and average heat capacities c 4 R and cp- 5 R. The cycle operates in a steady state with a substance flow rate of 0.375 mol s . Before the isothermal expansion (transition 1 - 2 at T1-T,-Thigh), l.e., after the adiabatic compression (transition 4 ? 1, from T4-Tlow to T-Thieh), the working fluid has a molar entropy given by s1 120.0 J K1 mol-". The Sackur-Tetrode equation, in differential form, is given by ds Rv1 dv + c,T1 dT a) What is the thermal efficiency of this reversible power cycle? b) Draw a T-s diagram with the four transitions and the four states of the cycle. c Beside s1, which is given, determine the molar entropy s2, S3, S& for the other three states

Answer 1

0 Net pouk output wc6 a) Thermal EAbcieney of evsibte pauc

匈 lo ul Thigt 500 느0, Cieuc Te constn Sicanst Zook it dout-

2-→ 3: 1Cotiqmal heat addition(+2%) (C) 们olah Cut oY of State, ie emol Euepy of State J-3 ← ck, dain ain

Goo 0.375 (5-4): 3 : S2 e.rur 2-8 기.nal k -)