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A gasoline engine has a power output of 180 \(\mathrm{kW}\) (about 241 \(\mathrm{hp} ) .\) Its thermal efficiency is 28.0\(\%\) (a) How much heat must be supplied to the engine per second? (b) How much heat is discarded by the engine per second?

Short Answer

Expert verified
(a) The heat supplied is 642.86 kW. (b) The heat discarded is 462.86 kW.

Step by step solution

01

Understand the Efficiency of the Engine

The thermal efficiency of the engine is given by the formula:\[ \text{Efficiency} = \frac{\text{Useful Power Output}}{\text{Heat Supplied}} \]Given that the efficiency is 28%, or 0.28 as a decimal, we need to find the heat supplied (\(Q_{in}\)). The useful power output \(P\) is 180 kW.
02

Calculate Heat Supplied

Rearrange the efficiency formula to solve for \(Q_{in}\):\[ Q_{in} = \frac{P}{\text{Efficiency}} \]Substitute the known values:\[ Q_{in} = \frac{180 \text{ kW}}{0.28} \]Calculate \(Q_{in}\):\[ Q_{in} = 642.86 \text{ kW} \] So, the heat supplied to the engine per second is approximately 642.86 kW.
03

Calculate Heat Discarded by the Engine

The heat discarded by the engine \(Q_{out}\) can be found using the equation:\[ Q_{out} = Q_{in} - P \]Substitute the known values:\[ Q_{out} = 642.86 \text{ kW} - 180 \text{ kW} \]Calculate \(Q_{out}\):\[ Q_{out} = 462.86 \text{ kW} \]Thus, the heat discarded by the engine per second is approximately 462.86 kW.

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Key Concepts

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

Heat Engines
Heat engines are devices that convert thermal energy into mechanical work. They work based on the principles of thermodynamics, typically using combustion of a fuel to heat a gas that then expands and performs work by moving pistons or turning a crankshaft. This expansion performs work, which can be used to power vehicles or generate electricity.
Heat engines operate in cycles, meaning they repeatedly go through a series of processes, such as compression, combustion, and exhaust. Each of these processes contributes to the overall efficiency of the engine.
Key characteristics of heat engines include:
  • They require a heat source (like a burning fuel) to operate.
  • They convert some of the heat supplied into work.
  • There is always some loss of heat, meaning not all the heat can be converted into useful work.
Understanding the fundamentals of how heat engines work is crucial when analyzing engine performance and efficiency.
Power Output
Power output is the measure of the engine's capability to perform work over time. For a gasoline engine, this is typically provided in kilowatts (kW) or horsepower (hp). It represents the usable energy that the engine provides for its intended purpose, like driving a car or generating electricity.
The power output of an engine is influenced by several factors, such as the engine's design, the type of fuel it uses, and its thermodynamic efficiency.
For example, in the exercise given, the engine's power output is 180 kW. This means that every second, the engine is capable of performing work equivalent to expending 180 kJ of energy in ideal conditions.
  • Power output is directly linked to how efficiently the engine can convert heat into work.
  • Maximizing power output while minimizing fuel consumption is often a key goal in engine design.
Engineers continuously work on improving engines to produce more power with less energy and resource waste.
Heat Transfer
Heat transfer in engines refers to the movement of thermal energy from the combustion of fuel to other components of the engine and eventually to the surroundings. It is a fundamental aspect that affects the performance and efficiency of heat engines.
There are typically three modes of heat transfer: conduction, convection, and radiation. In the context of an engine, most heat transfer occurs through conduction and convection.
  • Conduction allows heat to move through the solid parts of the engine from the hotter combustion chamber to the cooler components.
  • Convection allows heat to be transferred to the surrounding air or through a coolant system, which carries away unwanted thermal energy.
In the given exercise, understanding how much heat is supplied and discarded is important in calculating the efficiency of the engine. If too much heat is lost without being converted to work, the engine becomes less efficient. Therefore, engineers strive to optimize heat transfer processes to ensure as much thermal energy as possible is converted to useful work rather than lost. This often involves designing components that can withstand high temperatures and efficiently transfer heat where needed.

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Most popular questions from this chapter

A freezer has a coefficient of performance of \(2.40 .\) The freezer is to convert 1.80 \(\mathrm{kg}\) of water at \(25.0^{\circ} \mathrm{C}\) to 1.80 \(\mathrm{kg}\) of ice at \(-5.0^{\circ} \mathrm{C}\) in one hour. (a) What amount of heat must be removed from the water at \(25.0^{\circ} \mathrm{C}\) to convert it to ice at \(-5.0^{\circ} \mathrm{C} ?\) (b) How much much wasted heat is delivered to the room in which the freezer sits?

An aircraft engine takes in 9000 \(\mathrm{J}\) of heat and discards 6400 \(\mathrm{J}\) each cycle. (a) What is the mechanical work output of the engine during one cycle? (b) What is the thermal efficiency of the engine?

A Human Engine. You decide to use your body as a Carnot heat engine. The operating gas is in a tube with one end in your mouth (where the temperature is \(37.0^{\circ} \mathrm{C} )\) and the other end at the surface of your skin, at \(30.0^{\circ} \mathrm{C}\) . (a) What is the maximum efficiency of such a heat engine? Would it be a very useful engine? (b) Suppose you want to use this human engine to lift a 2.50 -kg box from the floor to a tabletop 1.20 \(\mathrm{m}\) above the floor. How much must you increase the gravitational potential energy, and how much heat input is needed to accomplish this? (c) If your favorite candy bar has 350 food calories \((1\) food calorie \(=4186 \mathrm{J})\) and 80\(\%\) of the food energy goes into heat, how many of these candy bars must you eat to lift the box in this way?

An air conditioner operates on 800 \(\mathrm{W}\) of power and has a performance coefficient of 2.80 with a room temperature of \(21.0^{\circ} \mathrm{C}\) and an outside temperature of \(35.0^{\circ} \mathrm{C}\) . (a) Calculate the rate of heat removal for this unit. (b) Calculate the rate at which heat is discharged to the outside air. (c) Calculate the total entropy change in the room if the air conditioner runs for 1 hour. Calculate the total entropy change in the outside air for the same time period. (d) What is the net change in entropy for the system (room + outside air)?

You decide to take a nice hot bath but discover that your thoughtless roommate has used up most of the hot water. You fill the tub with 270 \(\mathrm{kg}\) of \(30.0^{\circ} \mathrm{C}\) water and attempt to warm it further by pouring in 5.00 \(\mathrm{kg}\) of boiling water from the stove. (a) Is this a reversible or an irreversible process? Use physical reasoning to explain. (b) Calculate the final temperature of the bath water. (c) Calculate the net change in entropy of the system (bath water \(+\) boiling water), assuming no heat exchange with the air or the tub itself.

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