What Is Thermal Efficiency?

The meaning of thermal efficiency is that for a specific thermal energy conversion device, the ratio of the effective output energy to the input energy is a dimensionless index, which is generally expressed as a percentage. Commonly there are power generation devices, boiler devices, engine devices, etc. There are three definition methods: power generation efficiency, device efficiency, cycle efficiency. In boilers, generally small energy such as blowers, induced draft fans, and grate movements are not counted as input energy, but are calculated and measured separately.

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The thermal efficiency formula itself is related to the orderness index "entropy change" (represented by a simplified S).

s = A / Q = 1-(T2 / T1) Irregular editing

= 1-(T2 / Q1) S

If the micro-particles in the heat engine move in an orderly manner and develop in an orderly manner (do work), that is, entropy S 0, then (T2 / Q1) S 0,

s 1

If the movement of microscopic particles is disordered, 0 << 1.

If let Q be expressed by the total work energy of the system,

Q = 3PV or Q = U = 3PV

Thermal efficiency

0 = A / Q = PV / 3PV

= 1/3

He is a limit of the efficiency of traditional heat engines, that is why the efficiency of traditional heat engines is not easy to improve.

When the microscopic motion is orderly, we can know A = 3PV by and , so the efficiency of the new orderly power machine

s = A / Q = 3PV / 3PV

= 1

Obviously, the "hot" engine (engine) efficiency can reach or tend to 100% of the ideal value.

The efficiency of an energy substance or engine can be expressed as the ratio of work W or A to energy E or heat Q, that is,

= W / E = A / E

From the -- and - E = Q + W = PE + (1-P) E, W = A = (1-P) E, then

= 1-P = 1-Wi / = q

or

= 1-lnW / ln = -lnP / ln

= 1-S / kln

From the statistical entropy S = k`-`B`! `LnW, and P = W /

W = EXP (S / k`-`B`! `)

P = EXP (S / k`-`B`! `) /

Then efficiency can also be expressed in entropy

= 1-EXP (S / k`-`B`! `) /

Substituting P = 2/3 into the formula, we get the same result as = 1-Q`-`2`! `/ Q`-`1`!` = 1/3

= 1-P = 1-2 / 3 = 1/3

That is, the efficiency limit of a single-stage disordered heat engine is 1/3. For a multi-stage heat engine, the total energy Ei + 1 of the post-stage heat engine is the heat Qi emitted by the previous-stage heat engine, Ei + 1 = Qi; his efficiency is 1/3 of the efficiency of the previous-stage heat engine, i + 1 = i (1/3), then the compound efficiency of the n-stage heat engine

n = i

For n-class heat engines with i = 1/3, the limit of his compound efficiency

limn = lim 1/3 n = 1/2

n n

Only when P = 0, the micro-state of the system is highly ordered, and = 1-P = 1, the efficiency of the engine is 100%, which is the efficiency of a single-stage engine.

If you use a multi-stage engine, if you want to make the engine's efficiency reach 1, you only need the efficiency of each single-stage engine, that is, the degree of order is P = 1/2.

limn = lim 1/2 n = 1

Solve

If you only want to use a limited-stage engine to achieve 100% efficiency, you can use the compound efficiency formula and the sum of its proportional series S = a [(1-qn) / (1-q)] to derive The efficiency or order P of the required single-stage engine. Usually, a = q = and S = 1. When only two-stage engines are used, that is, n = 2, if the efficiency of the unit is to reach 100%, then S = a [(1-q2) / (1-q)]

2 + -1 = 0

`.` Solution

1 =-(1 + 51/2) / 2

2 = (51 / 2-1) / 2

Because 1, 0, we discard 1 =-(1 + 51/2) / 2 and keep the solution of = (51 / 2-1) / 2. That is, only the single-stage efficiency of the engine = (51 / 2-1) / 2 or P = 1- = (3-51 / 2) / 2 can make the combined efficiency of the two-stage ordered engine reach 100% . The incomplete order of this combination is much smaller than the fully ordered P = 1 due to the degree of order P = (3-51 / 2) / 2, so it is easier and more likely to implement than P = 1 Bigger. Other stages of engines can also be treated like this, and their single-stage efficiency is usually (3-51 / 2) / 2 <P <1/2 or (51 / 2-1) / 2 <; <1/2 between. Of course, the more efficient a single-stage ordered engine is

Obviously, under the two extreme conditions of P = 0 and P = 1, - and - are all valid. in

The results show the relationship between the system's state equation and the quantum energy formula under ideal conditions. Both the number of particles and the energy level of the system affect the work. The temperature of the system is also closely related to the energy of the system. Changes in the number of particles and energy levels in the system will cause changes in temperature.

The orderly decomposition of the internal energy sub-forms also gives a very important result: a more accurate and quantified thermal quantum form, and a deeper, updated definition of "heat": Q = P nii, Q = P (idni + nidi). It goes further than the traditional qualitative interpretation of "heat" and the understanding that "heat is the random movement of particles"-it can be quantified and deepens the understanding of the nature of heat, that is, heat is the energy of the quantum (particles) ( Energy level) and the degree of chaos (orderedness, entropy, distribution) of particle motion are closely related.

The energy or internal energy formula E = nii and its differential formula can be decomposed into the formula - like the first law of thermodynamics. Both heat and work are closely related to the system's entropy, degree of order q, or lnW / ln. The degree of order is the key to distinguish the internal energy or energy E = nii state, process and its evolution trend, and it is also the fundamental parameter for separating heat and work. He reflected and reflected the weight of heat and work, and changed the previous one-sided differential separation, and strengthened the connection between thermodynamics and mechanics. He is the bridge connecting heat and mechanics, and classical and modern thermodynamics. He decides whether the internal energy (energy) generates heat or does work and its size and efficiency. He revealed the internal relationship between the micro and macro order of the system and thermal and dynamic characteristics, established the relationship between micro particles and macro dynamic particles, and also linked the order to the efficiency of the engine. A new efficiency formula, = 1-P, is a new hope and theoretical basis for improving engine efficiency, changing the direction of engine research and development, and breaking the limit of heat engine efficiency 1/3 and 1/2. ^[1]