A diesel engine performs 2200 J of mechanical work and discards 4300 J of heat each cycle. (a) How much heat must be supplied to the engine in each cycle?

Verified step by step guidance

1. Identify the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system: \(\Delta U = Q - W\).
2. Recognize that for a complete cycle of an engine, the change in internal energy (\(\Delta U\)) is zero because the system returns to its initial state. Therefore, the equation simplifies to \(0 = Q - W\), or \(Q = W\).
3. Determine the total work done by the engine (W), which is the mechanical work output. In this case, it is given as 2200 J.
4. Calculate the total heat discarded by the engine, which is given as 4300 J. According to the conservation of energy, the heat supplied to the engine must account for both the work done and the heat discarded.
5. Set up the equation to find the heat supplied (\(Q_{supplied}\)) to the engine: \(Q_{supplied} = W + Q_{discarded}\). Substitute the values of W and Q to find \(Q_{supplied}\).

Key Concepts

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. In the context of a diesel engine, the work done by the engine and the heat exchanged must balance according to this principle. This law helps in understanding how the energy supplied to the engine is converted into mechanical work and heat.

Heat Transfer

Heat transfer refers to the movement of thermal energy from one object or system to another due to a temperature difference. In the case of the diesel engine, heat is supplied to the engine to facilitate combustion, and some of this energy is converted into work, while excess heat is discarded. Understanding heat transfer is crucial for calculating the total energy input required for the engine's operation.

Efficiency of Heat Engines

The efficiency of a heat engine is defined as the ratio of the work output to the heat input, often expressed as a percentage. It indicates how effectively the engine converts heat energy into mechanical work. In this scenario, knowing the efficiency helps determine how much heat must be supplied to achieve the desired work output, considering the heat lost during the cycle.