Understanding Indicated Thermal Efficiency

The indicated thermal efficiency is a key performance metric for internal combustion engines. It quantifies how efficiently the energy released from fuel combustion is converted into useful work done *inside* the engine cylinders (indicated work).

Definition of Indicated Thermal Efficiency

Indicated thermal efficiency, denoted as $\eta_{th,i}$, is defined as the ratio of the indicated power output ($P_i$) to the rate at which heat is supplied by the fuel ($\dot{Q}_{in}$) during the same time period.

• Indicated Power ($P_i$): The power developed from the pressure of combustion gases acting on the piston.
• Rate of Heat Supplied ($\dot{Q}_{in}$): The rate at which chemical energy from the fuel is released through combustion.

Formula for Indicated Thermal Efficiency

The relationship is expressed mathematically as:

$ \eta_{th,i} = \frac{P_i}{\dot{Q}_{in}} $

Analysis of Options

Let's examine the provided options based on this definition:

• Option 1: The ratio of brake power ($P_b$) to the rate of heat supplied ($\dot{Q}_{in}$). This defines brake thermal efficiency ($\eta_{th,b} = \frac{P_b}{\dot{Q}_{in}}$), not indicated thermal efficiency.
• Option 2: The ratio of indicated power ($P_i$) to the rate of heat supplied ($\dot{Q}_{in}$). This perfectly matches the definition of indicated thermal efficiency.
• Option 3: The ratio of mechanical efficiency ($\eta_m$) to indicated power ($P_i$). This is conceptually incorrect and dimensionally inconsistent.
• Option 4: The ratio of brake power ($P_b$) to indicated power ($P_i$). This defines mechanical efficiency ($\eta_m = \frac{P_b}{P_i}$).

Conclusion

Based on the fundamental definitions in internal combustion engine thermodynamics, the indicated thermal efficiency is correctly defined as the ratio of indicated power to the rate of heat supplied by the fuel.