Efficiency In A Thermodynamic Cycle
Question
The area on a PV diagram within one thermodynamic cycle of a heat engine is 610J. THe total thermal energy transferred out of the gas in one cycle is 1300J. Determine the efficiency of the cycle.
Attempt at solution
The area within the cycle is equivalent to the work done by the gas, which is 610J.
My first guess was just the ratio of the useful work done to the total, i.e $\frac$ to give about 32%. However, it turns out that the answer is just $\frac\approx 47\%$.
Thoughts
I thought that efficiency, intuitively, is the ratio of useful work to the total energy input
$$\text=\frac}}=\frac}$$
Alternatively, we could say that $$e=\frac-Q_}}=1-\frac}}$$These formulae seem intuitive, and I would be happy to apply them. But the question only gives us the value for $Q_$, so we don’t know $Q_$ or $Q_$
I just don’t see why the solution wants to find the ratio of work done to the thermal energy transferred out.
What you say is correct, you just misunderstand what data you are given.
There seems to be some confusion about the terms also, so let’s clear it out while looking at the schematic of a heat engine :
Personally I always use the terms $Q_$ and $Q_$ because it intuitively makes more sense to me to think of energy in and out. But all are used in different litterature.
From the drawing, which illustrates energy conservation, it of course makes sense that $$Q_=W+Q_\quad\Leftrightarrow\quad W=Q_-Q_$$
$$e=\frac}}=\frac}=\frac-Q_}}=1-\frac}}$$
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Fundamentals: The Physics Of Speed And Efficiency Of Growth
“If you give me a lever and a place to stand, I can move the worldâ Archimedes
In physics, a lever is a rigid object that is used with an appropriate fixed point to multiply the mechanical force that can be applied to another object. This is also known as the mechanical advantage and it’s an example of the principle of moments.
In addition to having discovered how to design machines capable of lifting enemy ships and creating efficient forms of defense and attack, Archimedes understood the power of speed, which gave way to the invention of weapons of mass attack against the Romans, guaranteeing numerous conquests for Syracuse.
When we explore the Universal Laws of Growth, we understand the general principles of biological, social and entrepreneurial growth, as well as the situations that happen for this growth becomes exponential. We also understand that when taking in inspiration from the Red Queen, the super-founders have two alternatives at their disposal by which to pursue exponentiality: brute force and intelligence.
Why are we so dedicated to growth? Because if we’re not growing, we’re dying. Why do we seek to promote this growth as quickly as possible? Because that’s the only way we can surprise the enemy. Why do we want to do this as efficiently as possible? Because resources are often scarce and valuable.
Principle #12: These principles apply to the three main business models used by startups: SaaS, Marketplaces and Direct-to-Consumer.
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How Do You Calculate Efficiency In Physics
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The work efficiency formula is efficiency = output / input, and you can multiply the result by 100 to get work efficiency as a percentage. This is used across different methods of measuring energy and work, whether it’s energy production or machine efficiency.
Secondly, what is the unit for efficiency? The efficiency is the energy output, divided by the energy input, and expressed as a percentage. A perfect process would have an efficiency of 100%. = efficiency Wout = the work or energy produced by a process. Units are Joules .
Also to know, how do you calculate building efficiency?
building efficiency. Percentage proportion of a building’s rentable area, not counting the area occupied by elevators, equipment, hallways, lobby, restrooms, etc. Formula: Rentable area x 100 ÷ Total floor area.
What is the formula for work?
The work is calculated by multiplying the force by the amount of movement of an object . A force of 10 newtons, that moves an object 3 meters, does 30 n-m of work. A newton-meter is the same thing as a joule, so the units for work are the same as those for energy joules.
How To Calculate Efficiency
In order to calculate efficiency, you need to apply the following formula:
= Eout / Ein * 100%
- is the efficiency ,
- Eout is the energy output , and
- Ein is the energy input .
The result will be a number between 0% and 100%. An efficiency equal to 0% means that all of the energy is wasted, and the energy output is equal to zero. On the other hand, an efficiency of 100% means that there is no waste of energy whatsoever.
The fundamental law of energy conservation states that you cannot create energy. What follows is that the efficiency of any machine can never exceed 100%. Nevertheless, you will probably come across articles saying that LED lights or heat pumps can have an efficiency of 300% or more.
How is it possible? The apparent efficiency of 300% results from the definition of efficiency that we use. The electrical power supplied to LED lights might be actually lower than the output, but it doesn’t mean that energy was created in the process. It merely means that the lights have received some heat energy from the surroundings and converted it into the output energy. As we aren’t able to measure this additional input, the apparent efficiency rises above 100%.
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What Is Wasted Energy In Physics
Wasted energyenergyEnergyEnergyenergy
What Is Efficiency In Physics Example
The more efficient the machine, the less energy wasted. For example, if a heat engine is able to turn 75 percent of the fuel it receives into motion, while 25 percent is lost as heat in the process, it would be 75 percent efficient. Out of the original 100 percent of the fuel, 75 percent was output as useful work.
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Conservation Of Mass And Of Energy
We often talk about burning calories in order to lose weight, but what does that really mean scientifically?. First, we really we mean lose mass that is the measure of how much stuff is in our bodies and weight depends on where you are . Second, our bodies cant just interchange mass and energy they arent the same physical quantity and dont even have the same units. So how do we actually lose mass by exercising? We dont actually shed the atoms and molecules that make up body tissues like fat by burning them. Instead, we break down the fat molecules into smaller molecules and then break bonds within those molecules to release chemical potential energy, which we eventually convert to work and exhaust heat. The atoms and smaller molecules that resulting from breaking the bonds combine to form carbon dioxide and water vapor and we breath them out. We also excrete a bit as H2O in sweat and urine. The process is similar to burning wood in campfire in the end you have much less mass of ash than you did original wood. Where did the rest of the mass go? Into the air as CO2 and H2O. The same is true for the fuel burned by your car. For more on this concept see the video below.
A YouTube element has been excluded from this version of the text. You can view it online here:
A YouTube element has been excluded from this version of the text. You can view it online here:
Efficient & Inefficient Systems
- Whenever energy is transferred from one form to another, some of that energy is usually wasted and is transferred away from the system, usually in the form of heat or waves
Whenever energy is transformed, some of the original energy usually ends up in an unwanted form
- An efficient system is one where most of the energy going into that system ends up in the form that is wanted Eg. An LED light bulb is efficient because most of the electrical energy ends up as light
- An inefficient system is one where most of the energy ends up in forms that werent wanted Eg. An old incandescent light bulb is inefficient because only a small amount of the electrical energy ends up as light
Sankey diagrams comparing modern and old light bulbs
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Solved Examples On Efficiency Formula
Question- A laborer puts in around 20 J of energy in one strike of his hammer on the nails head. The energy which the laborer inputs to drive the nail in the wood is 8.0 J. Calculate the efficiency of the laborers hammering?
Answer- We see over here that we have got our energy output as 8.0 J. Further, the energy input of the laborer is 20 J. Thus, we can calculate the efficiency by using the formula as below:
\ × 100%
\ = \ × 100%
\ = 0.40 × 100%
\ = 40%
Therefore, we see that the efficiency of the hammer strike was 40%. Vibrations and heating of the nail are two potential causes for the loss of energy.
Question- A certain process of the chemical has an energy efficiency of just 3.00%. In order to complete this chemical process on a large-scale, 140,000 J of energy is put in. Calculate the energy output of this process.
Answer- We see that we have energy input which is 140,000 J. We also know the efficiency as 3.00%. In order to calculate the energy output, we need to rearrange the formula for efficiency.
\ × 100% \ = \
\ = 4,200 J
Therefore, the energy output of this chemical process comes out as 4,200 J.
Can Pump Efficiency Be Greater Than 1
When you have a heat pump, you are comparing the amount of work needed to move heat from one reservoir to another with the amount of heat that is actually added to the target reservoir when the temperature difference is small, you only need a small amount of work to move a large amount of heat, so efficiency by
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What Is Efficiency In Physics For Kids
Efficiency is a measure of how much work or energy is conserved in a process. In many processes, work or energy is lost, for example as waste heat or vibration. The efficiency is the energy output, divided by the energy input, and expressed as a percentage. A perfect process would have an efficiency of 100%.
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Solving Problems Involving Efficiency
- Recall the two equations for calculating efficiency are:
- Which to use will depend on whether youre given a system calculating energies or power as shown in the examples below
Worked Example
The diagram shows a pump called a hydraulic ram.
In one such pump, the long approach pipe holds 700 kg of water. A valve shuts when the speed of this water reaches 3.5 m s-1 and the kinetic energy of this water is used to lift a small quantity of water by a height of 12m.
The efficiency of the pump is 20%.
Which mass of water could be lifted 12 m?
A. 6.2 kg B. 4.6 kg C. 7.3 kg D. 0.24 kg
- The pump is what converts the waters kinetic energy into gravitational potential energy
- Since its efficiency is 20%, you would multiply the kinetic energy by 0.2 since only 20% of the kinetic energy will be converted
Exam Tip
Equations for kinetic and potential energies are important for these types of questions. Also, familiarise yourself with the different equations for power depending on what quantities are given.
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What Is Energy Efficiency Physics
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Also asked, what is energy efficiency science?
Energy efficiency is how much energy is produced in a process versus the amount of energy given. For example, a light bulb is given a certain amount of electricity. Energy efficiency is about how much of that electricity gets turned into usable light.
Additionally, what is the formula for efficiency? Efficiency is often measured as the ratio of useful output to total input, which can be expressed with the mathematical formula r=P/C, where P is the amount of useful output produced per the amount C of resources consumed.
Also question is, what is useful energy in physics?
Useful energy. Useful energy is energy in the place we want it and the form we need it. Wasted energy is energy that is not useful enrgy. Useful energy and wasted energy both end up being transferred to the surroundings, ehich become warmer.
What is the use of efficiency?
Efficiency signifies a peak level of performance that uses the least amount of inputs to achieve the highest amount of output. It minimizes the waste of resources such as physical materials, energy, and time while accomplishing the desired output.
Selected Solutions To Problems & Exercises
1. 18.5 kJ 54.1%
3. 1.32 × 109 J 4.68 × 109 J
5. 3.80 × 109 J 0.667 barrels
7. 8.30 × 1012 J, which is 3.32% of 2.50 × 1014 J 8.30 × 1012 J, where the negative sign indicates a reduction in heat transfer to the environment.
- College Physics. : OpenStax College. Located at: . License: CC BY: Attribution. License Terms: Located at License
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Efficiency = Useful Power Out Total Power In
Efficiency has no units!
It can be written as a number between 0 and 1 or as a %. For example, an efficiency of 0.25 is the same as an efficiency of 25%.
Because some energy is always wasted from every device, efficiency should always be less than 1 or less than 100%. If you get answer that is bigger than 1 or 100%, you have made a mistake somewhere in your calculation!
Worked Examples
A power drill uses 500J of electricity. Only 400J of kinetic energy was generated by the drill. What is its efficiency?
A portable speaker coverts 150J of electrical energy into 30J of sound energy. Calculate its efficiency.
Efficiency Of A System
- The efficiency of a system is the ratio of the useful energy output from the system to the total energy input
- If a system has high efficiency, this means most of the energy transferred is useful
- If a system has low efficiency, this means most of the energy transferred is wasted
Efficiency equation in terms of energy
- Efficiency can also be written in terms of power :
Efficiency equation in terms of power
Worked Example
Exam Tip
Efficiency can be in a ratio or percentage format. If the question asks for an efficiency as a ratio, give your answer as a fraction or decimal. If the answer is required as a percentage, remember to multiply the ratio by 100 to convert it, e.g. Ratio = 0.25, Percentage = 0.25 × 100 = 25 %
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The First Law Of Thermodynamics
The Principle of Conservation of Energy states that energy cannot be created or destroyed. Therefore, if the body does useful work to transfer mechanical energy to its surroundings , or transfer thermal energy to the environment as heat, then that energy must have come out of the bodys internal energy. We observe this in nature as the First Law of Thermodynamics:
Your body uses chemical potential energy stored internally to do work, and that process also generates thermal energy, which you release as exhaust heat. The internal combustion engines that power most cars operate in similar fashion by converting chemical potential energy in fuel to thermal energy via combustion, then converting some of the thermal energy into useful work and some into exhaust heat. Your body is capable of releasing the chemical potential energy in your food without combustion, which is good, because you are not capable of using thermal energy your from yourinternal energy to do work. Machines that can use thermal energy to do work, such as a combustion engine, are known as heat engines. Heat engines are still governed by the First Law of Thermodynamics, so any exhaust heat must have been thermal energy that was not used to do work. The thermal energy input that can be used to do work rather than wasted as exhaust heat determines the efficiency of the heat engine.
Reinforcement Exercises
You apply a 50 N force in order to slide an object 3 m. How much useful work did you do?