A diesel engine performs 22002200 J of mechanical work and discards 43004300 J of heat each cycle. How much heat must be supplied to the engine in each cycle?

Ch 20: The Second Law of Thermodynamics

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th Edition

Ch 20: The Second Law of Thermodynamics

Problem 1a

Chapter 20, Problem 1a

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

Verified step by step guidance

Understand the problem: We need to find out how much heat is supplied to the diesel engine in each cycle. We know the engine performs 2200 J of mechanical work and discards 4300 J of heat.

Recall the first law of thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W): ΔU = Q - W.

In a cyclic process, the change in internal energy (ΔU) over one complete cycle is zero because the system returns to its initial state. Therefore, we can set ΔU = 0 in the equation: 0 = Q - W.

Rearrange the equation to solve for the heat supplied (Q): Q = W + ΔU. Since ΔU = 0, the equation simplifies to Q = W.

Substitute the given values into the equation: Q = 2200 J (work done) + 4300 J (heat discarded). This will give you the amount of heat that must be supplied to the engine in each cycle.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

First Law of Thermodynamics

The First Law of Thermodynamics, also known as the law of energy conservation, states that energy cannot be created or destroyed, only transformed. In the context of engines, it implies that the energy input (heat supplied) equals the sum of the energy output (work done) and the energy discarded as waste heat.

Heat Engine Efficiency

Heat engine efficiency is a measure of how well an engine converts heat into work. It is calculated by dividing the work output by the heat input. Understanding efficiency helps in determining the amount of heat required to perform a certain amount of work, considering the heat discarded.

Energy Balance in Cycles

Energy balance in cycles refers to the equilibrium between energy input, work output, and waste heat in a cyclic process. For a diesel engine, the energy supplied as heat must equal the sum of mechanical work done and heat discarded, ensuring the cycle adheres to the conservation of energy principle.

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The coefficient of performance $K = H / P$ is a dimensionless quantity. Its value is independent of the units used for $H$ and $P$ , as long as the same units, such as watts, are used for both quantities. However, it is common practice to express $H$ in Btu/h and $P$ in watts. When these mixed units are used, the ratio $H / P$ is called the energy efficiency ratio ( $E E R$ ). If a room air conditioner has $K equals 3.0$ , what is its $E E R$ ?

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Calculate the theoretical efficiency for an Otto-cycle engine with $g equals 1.40$ and $r equals 9.50$ .

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The Otto-cycle engine in a Mercedes-Benz SLK230 has a compression ratio of $8.8$ . What is the ideal efficiency of the engine? Use $g equals 1.40$ .

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