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In the Otto cycle, heat addition occurs during the constant volume process from state 2 to state 3. This is when the fuel-air mixture combusts, significantly increasing the temperature and pressure of the air. To calculate heat addition, use the formula \[ Q_{in} = m(u_3 - u_2) \] where \( m \) is the mass of air and \( u_3 \) and \( u_2 \) are the internal energies at states 3 and 2, respectively. In our example, we use the internal energies from the table to find: \[ Q_{in} = 0.002 \times (725.02 - 486.77) = 0.4765 \text{ kJ} \] This heat addition provides the necessary energy for the air to expand and perform work during the cycle. Simple, right?

Heat rejection in the Otto cycle occurs during the constant volume process from state 4 to state 1. This is when heat is removed from the system, reducing the temperature and pressure of the air. The formula for heat rejection is \[ Q_{out} = m(u_4 - u_1) \] where \( m \) is the mass of air and \( u_4 \) and \( u_1 \) are the internal energies at states 4 and 1. In our case: \[ Q_{out} = 0.002 \times (329.01 - 217.67) = 0.2227 \text{ kJ} \] This heat ejected helps bring the air back to its initial state, ready to start a new cycle.

The net work ( \( W_{net} \) ) done by the Otto cycle is the difference between the heat added and the heat rejected. Simply put, it is the energy output we get from the cycle. The formula is \[ W_{net} = Q_{in} - Q_{out} \] Substituting our previously calculated values, we get: \[ W_{net} = 0.4765 \text{ kJ} - 0.2227 \text{ kJ} = 0.2538 \text{ kJ} \] This net work indicates the useful energy obtained from the cycle, which can be used to drive mechanical processes.

Thermal efficiency ( \( \eta \) ) of the Otto cycle quantifies how effectively the cycle converts the heat input into useful work. It is calculated using: \[ \eta = \frac{W_{net}}{Q_{in}} \] Simply put, it’s the ratio of the net work to the heat added. From our example: \[ \eta = \frac{0.2538 \text{ kJ}}{0.4765 \text{ kJ}} = 0.5325 \text{ or } 53.25\text{ \textpercent} \] This means 53.25% of the heat added is converted into useful work, while the rest is rejected as waste heat. Higher thermal efficiency indicates a more efficient cycle.

Mean effective pressure (MEP) is a hypothetical pressure that, if applied uniformly over the entire piston area during the power stroke, would produce the same amount of net work output as the actual cycle. It’s calculated using: \[ MEP = \frac{W_{net}}{V_{dis}} = \frac{W_{net}}{V_1 - V_2} \] To find MEP, we need to calculate the displacement volume ( \( V_{dis} \) ), which depends on the volumes at states 1 and 2. Given the relationship, \( p V = m R T \) , where \( R \) is the gas constant, we can determine the specific volumes and thus \( V_1 \) and \( V_2 \). Once we have these, we substitute them into the formula to find MEP. This value gives a sense of the engine’s efficiency in terms of pressure and is crucial in engine design and analysis.