Answer to Question #183628 in Mechanical Engineering for randz

Question #183628

2. An ideal Otto engine, operating on the hot-air standard with k=1.34, has a compression ratio of 5. At

the beginning of compression the volume is 12 m 3 , the pressure is 95 kPaa and temperature is 38 oC.

During constant – volume heating, 370 kJ are added per cycle. Compute T 3 , P 3 , T 4 , Qa, Qr, Wnet,

thermal Efficiency, and mean effective pressure.


1
Expert's answer
2021-04-23T08:25:26-0400

Given :

"\\gamma = 1.34"

"r_k = 5"

"V_1= 12 m^3" "V_2 = \\frac {V_1}{r_k} = \\frac {12}{5}=2.4 m^3"

"P_1=95kPa"

"T_1 = 38^0C = 311^0K"

"Q_s = 370 kJ"

"\\eta=1-\\frac{1}{r_k^{\\gamma- 1}} = 1-\\frac{1}{5^{1.34- 1}} = 0.4214 = 42.14" %


for "T_2= T_1({\\frac{V_1}{V_2}})^{\\gamma -1} = 311 \\times 5^{0.34} = 537.53^0K"


"Q_s = mC_v(T_3-T_2)"


"370 = 1\\times 0.718\\times(T_3-537.53)"


"T_3 =1052.85 ^0C"


"\\frac{T_3}{T_4}=(r_k)^{\\gamma-1}"


"T_4 =\\frac{1052.85}{5^{0.34}}= 609.139^0K"


"P_2 = P_1\\times (r_k)^{\\gamma-1} = 95(5)^0.34=164.2 kPa"


"P_3 = \\frac{T_3}{T_2}\\times P_2 = \\frac{1052.85}{537.53}\\times 164.2 =321.61kPa"


"Q_r = mC_v(T_4-T_1)= 1\\times 0.718\\times (609.139-311) =214.06 KJ"


"W_{Net}=Q_s-Q_r = 370 - 214.06 =155.94 \\frac{kJ}{kg}"


"MEP = \\frac{W_{net}}{V_1-V_2} = \\frac {155.94}{12-2.4} =16.24kPa"



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