Question

The heat input to an Otto cycle is 1000kJ/kg. The compression ratio is 8 and the pressure and temperature at the beginning of the compression stroke are 100kPa and 15°C. Determine a. The maximum temperature and pressure in the cycle b. The thermal efficiency of the cycle C. The net work output d. The mean effective pressure

Answer 1

Answer:

a. $T_3=2027.1 K,P_3=5750.22 KPa$  

b. $\eta =0.564$

c. Work out put = 564 KJ/kg

d. $P_{mean}=786.61 KPa$

Explanation:

Given that

Heat in put = 1000 KJ/kg

Compression ratio,r = 8

$T_1=15 C$  

$P_1=100 KPa$  

Process 1-2

$\dfrac{T_2}{T_1}=r^{\gamma -1}$

$\dfrac{T_2}{273+15}=8^{1.4 -1}$

$T_2=661.65 K$  

$\dfrac{P_2}{P_1}=r^{\gamma}$

$\dfrac{P_2}{100}=8^{1.4}$

$P_2=1837.9 KPa$  

Process 2-3

We know that for air

$C_v=0.71\ \frac{KJ}{kg-K}$

$Q=C_v(T_3-T_2)$

$1000=0.71(T_3-661.5)$

$T_3=2027.1 K$  

$\dfrac{P_3}{P_2}=\dfrac{T_3}{T_2}$

$\dfrac{P_3}{1837.9}=\dfrac{2027.1}{661.5}$

$P_3=5750.22 KPa$  

We know that efficiency of otto cycle  

$\eta =1-\dfrac{1}{r^{\gamma -1}}$

$\eta =1-\dfrac{1}{8^{1.4-1}}$

$\eta =0.564$

$\eta =\dfrac{Work\ out\ put}{Heat\ in\ put}$

$0.564 =\dfrac{Work\ out\ put}{1000}$

Work out put = 564 KJ/kg

$v_1=\dfrac{RT_1}{P_1}$

$v_1=\dfrac{0.287\times 288}{100}$

$v_1=0.82656\ \frac{m^3}{kg}$

So

$v_2=\dfrac{0.82656}{8}\ \frac{m^3}{kg}$

$v_2= 0.103\frac{m^3}{kg}$

$Work\ out\ put\ = P_{mean}\times (v_1-v_2)$

$564= P_{mean}\times (0.82-0.103)$

$P_{mean}=786.61 KPa$