Answer to Question #99296 in Electrical Engineering for Hardi Amiru Sulemana

Question

An engine operating on the outo cycle has a compression ratio of 7.5:1. At the beginning of the compression stroke,the air is at 1.035bar and 27°C. If the heat energy supplied is 930Kj/kg of air, calculate; the maximum temperature and pressure in the cycle and the cycle efficiency

Answer 1

The Otto cycle consists of four stages:

1-2: adiabatic compression;

2-3: isochoric compression;

3-4: adiabatic expansion;

4-1: isochoric cooling.

Calculate the cycle thermal efficiency (for the air at the temperature of 27°C k=1.4):

$$\eta_{th}=1-\frac{1}{r^{k-1}}=1-\frac{1}{7.5^{1.4-1}}=0.553.$$

At the end of the adiabatic compression:

$$T_2=T_1r^{k-1}=(273+27)7^{1.4-1}=671\text{ K}.$$

The pressure at 2 is

$$p_2=r\frac{T_2}{T_1}p_1=7.5\cdot\frac{671}{300}\cdot101325=1736213\text{ Pa}.$$

The isochoric heat capacity:

$$c_V=2.5\cdot0.2871=0.71775\text{ kJ/(kg-K)}.$$

The heat energy supplied:

$$930=q=c_V(T_3-T_2),$$

here $T_3$ is the maximum temp:

$$T_3=\frac{q}{C_V}+T_2=\frac{930}{0.71775}+653=1949\text{ K}.$$

During the isochoric stage 2-3 the pressure reaches its maximum as well:

$$\frac{p_2}{T_2}=\frac{p_3}{T_3},\\ \space\\ p_3=p_2\frac{T_3}{T_2}=1736213\frac{1949}{653}=5043038\text{ Pa},$$

or 50.4 bar.