Diesel and gasoline engines: comparison of efficiency. Efficiency

Definition

Mathematically, the definition of efficiency can be written as:

Where A- useful work (energy), and Q- energy expended.

If efficiency is expressed as a percentage, then it is calculated by the formula:

Where Q X (\displaystyle Q_(\mathrm (X) ))- heat taken from the cold end (in refrigeration machines, cooling capacity); A (\displaystyle A)

The term used for heat pumps is transformation ratio

Where Q Γ (\displaystyle Q_(\Gamma ))- condensation heat transferred to the coolant; A (\displaystyle A)- the work (or electricity) spent on this process.

In the perfect car Q Γ = Q X + A (\displaystyle Q_(\Gamma )=Q_(\mathrm (X) )+A), from here to the ideal car ε Γ = ε X + 1 (\displaystyle \varepsilon _(\Gamma )=\varepsilon _(\mathrm (X) )+1)

The reverse Carnot cycle has the best performance indicators for refrigeration machines: it has a coefficient of performance

Where T Γ (\displaystyle T_(\Gamma )), T X (\displaystyle T_(\mathrm (X) )) -

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  Mathematically, the definition of efficiency can be written as:

  η = A Q , (\displaystyle \eta =(\frac (A)(Q)),)

  Where A- useful work (energy), and Q- energy expended.

  If efficiency is expressed as a percentage, then it is calculated by the formula:

  η = A Q × 100% (\displaystyle \eta =(\frac (A)(Q))\times 100\%) ε X = Q X / A (\displaystyle \varepsilon _(\mathrm (X) )=Q_(\mathrm (X) )/A),

  Where Q X (\displaystyle Q_(\mathrm (X) ))- heat taken from the cold end (in refrigeration machines, cooling capacity); A (\displaystyle A)

  The term used for heat pumps is transformation ratio

  ε Γ = Q Γ / A (\displaystyle \varepsilon _(\Gamma )=Q_(\Gamma )/A),

  Where Q Γ (\displaystyle Q_(\Gamma ))- condensation heat transferred to the coolant; A (\displaystyle A)- the work (or electricity) spent on this process.

  In the perfect car Q Γ = Q X + A (\displaystyle Q_(\Gamma )=Q_(\mathrm (X) )+A), from here to the ideal car ε Γ = ε X + 1 (\displaystyle \varepsilon _(\Gamma )=\varepsilon _(\mathrm (X) )+1)

  The reverse Carnot cycle has the best performance indicators for refrigeration machines: it has a coefficient of performance

  ε = T X T Γ − T X (\displaystyle \varepsilon =(T_(\mathrm (X) ) \over (T_(\Gamma )-T_(\mathrm (X)))), because, in addition to the energy taken into account A(e.g. electric), in heat Q There is also energy taken from the cold source.

  Let's say we are relaxing at the dacha, and we need to fetch water from the well. We lower the bucket into it, scoop up the water and begin to lift it. Have you forgotten what our goal is? That's right: get some water. But look: we are lifting not only the water, but also the bucket itself, as well as the heavy chain on which it hangs. This is symbolized by a two-color arrow: the weight of the load we lift is the sum of the weight of the water and the weight of the bucket and chain.

  Considering the situation qualitatively, we will say: along with the useful work of raising water, we also perform other work - lifting a bucket and chain. Of course, without the chain and bucket we would not be able to draw water, but from the point of view of the ultimate goal, their weight “harms” us. If this weight were less, then complete perfect work would also be smaller (with the same usefulness).

  Now let's move on to quantitative studying these works and introduce a physical quantity called efficiency.

  Task. The loader pours the apples selected for processing from the baskets into the truck. The mass of an empty basket is 2 kg, and the apples in it are 18 kg. What is the share of the loader's useful work from his total work?

  Solution. The full job is moving apples in baskets. This work consists of lifting apples and lifting baskets. Important: lifting apples is useful work, but lifting baskets is “useless”, because the purpose of the loader’s work is to move only the apples.

  Let us introduce the notation: Fя is the force with which the hands lift only apples up, and Fк is the force with which the hands lift only the basket up. Each of these forces is equal to the corresponding force of gravity: F=mg.

  Using the formula A = ±(F||· l) , we “write out” the work of these two forces:

  Auseful = +Fя · lя = mя g · h and Аuseless = +Fк · lк = mк g · h

  The total work consists of two works, that is, it is equal to their sum:

  Afull = Auseful + Auseless = mя g h + mк g h = (mя + mк) · g h

  In the problem we are asked to calculate the share of the loader's useful work from his total work. Let's do this by dividing the useful work by the total:

  In physics, such shares are usually expressed as percentages and denoted by the Greek letter “η” (read: “this”). As a result we get:

  η = 0.9 or η = 0.9 100% = 90%, which is the same.

  This number shows that out of 100% of the loader's total work, the share of his useful work is 90%. The problem is solved.

  Physical quantity equal to the ratio iyu useful work to total work done, in physics has its own name - efficiency - efficiency:

  After calculating the efficiency using this formula, it is usually multiplied by 100%. And vice versa: to substitute efficiency into this formula, its value must be converted from percent to decimal fraction, dividing by 100%.

  Efficiency is a characteristic of the operating efficiency of a device or machine. Efficiency is defined as the ratio of the useful energy at the output of the system to the total amount of energy supplied to the system. Efficiency is a dimensionless value and is often determined as a percentage.

  Formula 1 - efficiency

  Where- A useful work

  —Q total work that was spent

  Any system that does any work must receive energy from outside, with the help of which the work will be done. Take, for example, a voltage transformer. A mains voltage of 220 volts is supplied to the input, and 12 volts is removed from the output to power, for example, an incandescent lamp. So the transformer converts the energy at the input to the required value at which the lamp will operate.

  But not all the energy taken from the network will reach the lamp, since there are losses in the transformer. For example, losses of magnetic energy in the core of a transformer. Or losses in the active resistance of the windings. Where electrical energy will be converted into heat without reaching the consumer. This thermal energy is useless in this system.

  Since power losses cannot be avoided in any system, the efficiency is always below unity.

  Efficiency can be considered for the entire system, consisting of many individual parts. So, if you determine the efficiency for each part separately, then the total efficiency will be equal to the product of the efficiency coefficients of all its elements.

  In conclusion, we can say that efficiency determines the level of perfection of any device in the sense of transmitting or converting energy. It also indicates how much energy supplied to the system is spent on useful work.

  Physics is a science that studies processes occurring in nature. This science is very interesting and curious, because each of us wants to satisfy ourselves mentally by gaining knowledge and understanding of how and what works in our world. Physics, the laws of which have been deduced over centuries and by dozens of scientists, helps us with this task, and we should only rejoice and absorb the knowledge provided.

  But at the same time, physics is a far from simple science, like, in fact, nature itself, but it would be very interesting to understand it. Today we will talk about efficiency. We will learn what efficiency is and why it is needed. Let's look at everything clearly and interestingly.

  Explanation of the abbreviation - efficiency. However, this interpretation may not be particularly clear the first time. This coefficient characterizes the efficiency of a system or any individual body, and more often, a mechanism. Efficiency is characterized by the output or conversion of energy.

  This coefficient applies to almost everything that surrounds us, and even to ourselves, and to a greater extent. After all, we do useful work all the time, but how often and how important it is is another question, and the term “efficiency” is used with it.

  It is important to consider that this coefficient is an unlimited value, it usually represents either mathematical values, for example, 0 and 1, or, as is more often the case, as a percentage.

  In physics, this coefficient is denoted by the letter Ƞ, or, as it is commonly called, Eta.

  

  Useful work

  When using any mechanisms or devices, we necessarily perform work. As a rule, it is always greater than what we need to complete the task. Based on these facts, two types of work are distinguished: expended, which is denoted by a capital letter, A with a small z (Az), and useful - A with the letter p (An). For example, let's take this case: we have a task to lift a cobblestone with a certain mass to a certain height. In this case, work characterizes only overcoming the force of gravity, which, in turn, acts on the load.

  In the case when any device other than the gravity of the cobblestone is used for lifting, it is also important to take into account gravity of the parts of this device. And besides all this, it is important to remember that while we win in strength, we will always lose along the way. All these facts lead to one conclusion that the work expended in any case will be more useful, Az > An, the question is how much more it is, because you can reduce this difference as much as possible and thereby increase the efficiency, ours or our device.

  Useful work is the portion of expended work that we do using a mechanism. And efficiency is precisely the physical quantity that shows what part of the useful work is from the total work expended.

  Result:

  • The expended work Az is always greater than the useful work Ap.
  • The greater the ratio of useful to expended, the higher the coefficient, and vice versa.
  • Ap is found by multiplying the mass by the acceleration of gravity and the height of ascent.

  

  There is a certain formula for finding efficiency. It goes like this: to find efficiency in physics, you need to divide the amount of energy by the work done by the system. That is, efficiency is the ratio of energy expended to work performed. From this we can draw a simple conclusion that the better and more efficient the system or body is, the less energy is spent on doing the work.

  The formula itself looks short and very simple: it will equal A/Q. That is, Ƞ = A/Q. This brief formula captures the elements we need for calculation. That is, A in this case is the used energy that is consumed by the system during operation, and the capital letter Q, in turn, will be the spent A, or again the spent energy.

  Ideally, the efficiency is equal to unity. But, as usually happens, he is smaller than her. This happens because of physics and because, of course, the law of conservation of energy.

  The thing is that the law of conservation of energy suggests that more A cannot be obtained than energy received. And even this coefficient will be equal to one extremely rarely, since energy is always wasted. And work is accompanied by losses: for example, in an engine, the loss lies in its excessive heating.

  So, the efficiency formula:

  Ƞ=A/Q, Where

  • A is the useful work the system performs.
  • Q is the energy consumed by the system.

  Application in various fields of physics

  It is noteworthy that efficiency does not exist as a neutral concept, each process has its own efficiency, it is not a friction force, it cannot exist on its own.

  Let's look at some examples of processes with efficiency.

  Eg, let's take an electric motor. The job of an electric motor is to convert electrical energy into mechanical energy. In this case, the coefficient will be the efficiency of the engine in terms of converting electrical energy into mechanical energy. There is also a formula for this case, and it looks like this: Ƞ=P2/P1. Here P1 is the power in the general version, and P2 is the useful power that the engine itself produces.

  It is not difficult to guess that the structure of the coefficient formula is always preserved, only the data that needs to be substituted in it changes. They depend on the specific case, if it is an engine, as in the case above, then it is necessary to operate with the power expended, if it is a job, then the initial formula will be different.

  

  Now we know the definition of efficiency and we have an idea about this physical concept, as well as about its individual elements and nuances. Physics is one of the largest sciences, but it can be broken down into small pieces to understand it. Today we examined one of these pieces.

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