Question

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.

Answer 1

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

$Q_s = mC_v(T_3-T_2)$

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

$T_3 =1052.85 ^0C$

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

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

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

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

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

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

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