# Step-by-Step Solution Let's break down what each term means and how they relate to each other: ## Given Data - **Rated Engine Power**: This is the **Brake Power (BP)** at the rated speed. - **Rated Engine Speed**: The speed (in RPM) at which the rated power is measured. - **Indicated Thermal Efficiency (\(\eta_{th,ind}\))**: Efficiency of converting fuel energy to indicated power. - **Mechanical Efficiency (\(\eta_{mech}\))**: Efficiency of converting indicated power to brake power. ## Key Definitions - **Brake Power (BP)**: The usable power output at the crankshaft. - **Indicated Power (IP)**: Power developed inside the combustion chamber. - **Friction Power (FP)**: Power lost to friction, \(FP = IP - BP\). - **Fuel Equivalent Power (FEP)**: Power that would result if all fuel energy input were converted to power. ## Relationships 1. **Mechanical Efficiency**: \[ \eta_{mech} = \frac{BP}{IP} \implies IP = \frac{BP}{\eta_{mech}} \] 2. **Indicated Thermal Efficiency**: \[ \eta_{th,ind} = \frac{IP}{\text{Fuel Energy Input}} \implies \text{Fuel Energy Input} = \frac{IP}{\eta_{th,ind}} \] - Fuel Equivalent Power is often synonymous with Fuel Energy Input. 3. **Friction Power**: \[ FP = IP - BP \] --- ## What Can You Calculate? ### 1. **Indicated Power (IP)** - Given \( BP \) (Rated Engine Power) and \( \eta_{mech} \): \[ IP = \frac{BP}{\eta_{mech}} \] ### 2. **Friction Power (FP)** - Once you have \( IP \), \( FP = IP - BP \). ### 3. **Fuel Equivalent Power** - Once you have \( IP \) and \( \eta_{th,ind} \): \[ \text{Fuel Equivalent Power} = \frac{IP}{\eta_{th,ind}} \] --- ## Evaluating the Choices - **You can calculate Friction Power and Indicated Power** **True** (from the equations above). - **You can calculate Indicated Power and Fuel Equivalent Power** **True** (see equations above). - **All are True** This statement would only be correct if every individual option is true. Let's check the last one. - **None are True** **False**, as you can calculate the above values. - **You can calculate Indicated Power and Fuel Equivalent Power** **True** (already addressed). --- ## Final Answer **All are True** ### Explanation Given the Brake Power (Rated Engine Power), Indicated Thermal Efficiency, and Mechanical Efficiency, you can calculate: - Indicated Power (IP) - Friction Power (FP) - Fuel Equivalent Power Therefore, **"All are True"** is the best answer. --- ## Summary Table | Quantity | Formula | |---------------------------|--------------------------------| | Indicated Power (IP) | \( IP = \frac{BP}{\eta_{mech}} \) | | Friction Power (FP) | \( FP = IP - BP \) | | Fuel Equivalent Power | \( \frac{IP}{\eta_{th,ind}} \) | --- **Correct Choice:** **All are True**