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(I) A heat engine does 9200 J of work per cycle while absorbing 25.0 kcal of heat from a high-temperature reservoir. What is the efficiency of this engine?

Short Answer

Expert verified
The efficiency of the engine is approximately 8.79%.

Step by step solution

01

Understand the Concepts

The efficiency of a heat engine is defined as the ratio of the work output to the heat input, expressed as a percentage. The formula can be given as \( \text{Efficiency} = \left( \frac{W}{Q_H} \right) \times 100\% \), where \(W\) is the work done and \(Q_H\) is the heat absorbed from the high-temperature reservoir.
02

Convert the Heat Input

The heat absorbed from the reservoir is given in kilocalories, but we need it in joules to use it in our calculation. The conversion factor is \(1 \text{kcal} = 4184 \text{J}\). Thus, \(Q_H = 25.0 \text{kcal} \times 4184 \text{J/kcal} = 104600 \text{J}\).
03

Calculate the Efficiency

Substitute the values of work done \(W = 9200 \text{J}\) and heat absorbed \(Q_H = 104600 \text{J}\) into the efficiency formula: \[ \text{Efficiency} = \left( \frac{9200}{104600} \right) \times 100\% \] Calculate the efficiency to get approximately 8.79\%.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Thermodynamics
Thermodynamics is the branch of physics that deals with heat, work, and the forms of energy related to them. One of the fundamental concepts in thermodynamics is the idea of a heat engine. A heat engine is a system that converts thermal energy into work. This conversion involves absorbing heat from a high-temperature source, performing work, and then releasing some of the heat to a low-temperature sink.
This process is governed by the laws of thermodynamics, specifically the first and second laws. The first law, also known as the conservation of energy, states that energy cannot be created or destroyed, only transformed from one form to another. The second law introduces the concept of entropy and dictates the direction of heat transfer. It essentially tells us that heat flows spontaneously from hot to cold, a principle utilized by heat engines.
Work-Energy Relation
The work-energy relation is crucial in understanding how heat engines function. In physics, work is defined as the energy transferred when an object is moved by a force. In the context of a heat engine, work is the useful mechanical energy output generated by the engine.
For a heat engine, we have an input in the form of heat energy and an output in the form of work energy. The efficiency of this energy conversion is a measure of how well the engine transforms heat into work. Additionally, the work-energy principle complements this understanding by stating that the work done on or by a system is equal to the change in the system's kinetic energy.
  • Work done by a heat engine: the force applied or the movement created by the engine.
  • Relation to energy: understanding how much energy has been converted to perform a specific task or create motion.
Energy Conversion
Energy conversion is the process of changing energy from one form to another. In a heat engine, this involves converting thermal energy from the heat absorbed into mechanical energy by producing work.
Every energy conversion process comes with a certain degree of efficiency, whereby not all the input energy is converted into a useful form. Some of the energy is inevitably lost, usually in the form of waste heat. This inefficiency is the basis of why heat engines cannot reach perfect efficiency.
It's important to note that energy can neither be created nor destroyed, as per the law of conservation of energy. Therefore, the energy conversion processes are more about transforming energy rather than producing or losing it altogether. Engineers often focus on optimizing these processes to improve efficiency.
Heat Transfer
Heat transfer is the movement of heat from one body or material to another. This can occur through conduction, convection, or radiation. In the functioning of heat engines, heat transfer is a vital process that ensures the engine operates efficiently.
  • Conduction occurs when heat is transferred through a solid material, often leading to unwanted energy losses if the material is not properly insulated.
  • Convection transfers heat through a fluid, which can be a liquid or a gas. It's the principle used in many cooling systems for heat engines.
  • Radiation transfers heat through electromagnetic waves and does not require a medium, although it's more common in high-temperature engines.
The efficiency and effectiveness of a heat engine are significantly influenced by how well it manages heat transfer. Engine designs often aim to maximize heat absorption from the source and minimize wastage during the transfer processes.

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Most popular questions from this chapter

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