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Thermodynamics&

Heat transferLecture 05

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Instructor: Dr. Qari Khalid Waheed

Institute of Mechatronics Engineering,

UET Peshawar.

BY: Engr. Muhammad Usman Khan

(MtE-203)

Fall 2015

The Heat Engine Cycle

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The Carnot Cycle:The ideal theoretical cycle which is the most efficient conceivable is known

as Carnot cycle.

The highest thermal efficiency possible for a heat engine in practice is only about half that of the ideal theoretical Carnot cycle, between the same temperature limits.Due to irreversibilities in the actual cycle, and to deviations from ideal cycle

Carnot showed that the most efficient possible cycle is one in which all the heat supplied is supplied at one fixed temperature, and all the heat rejected is rejected at a lower fixed temperature.

The cycle therefore consists of two isothermal processes joined by two adiabatic processes.

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Fig 1: Carnot cycle on a T-s diagram

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The Carnot Cycle (cont’d)

In Fig. 1:

Process 1 to 2 is isentropic expansion from T1 to T2.

Process 2 to 3 is isothermal heat rejection.

Process 3 to 4 is isentropic compression from T2 to T1.

Process 4 to 1 is isothermal heat supply.

The cycle is completely independent of the working substance used.

The cycle efficiency is given by:

Ƞ = - 𝑾/Q1

= 𝑸/Q1

Example 5.1

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Fig 2: Carnot cycle for a wet vapour on a T-s diagram

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The Carnot Cycle for a perfect gas

In Fig. 1:

Process 1 to 2 is isentropic expansion from T1 to T2.

Process 2 to 3 is isothermal heat rejection.

Process 3 to 4 is isentropic compression from T2 to T1.

Process 4 to 1 is isothermal heat supply.

The cycle is completely independent of the working substance used.

The cycle efficiency is given by:

Ƞ = - 𝑾/Q1

= 𝑸/Q1

Example 5.1

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Absolute Temperature Scale

Using the scale of thermodynamics it is possible to establish a temp. Scale which is independent of the working substance.

Where:

ᶲ is a function and X1 & X2 are the temp. of hot and cold reservoirs.

Combining these two equations we have:

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Absolute Temperature Scale (cont’d)

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• After selecting a suitable temp. scale we have the equation as:

• Now from the Equation. Of Carnot Cycle we have:

• Hence we have:

• Thus from this equation we have temp. X is equal to T. Thus by using a

suitable function ᶲ we have the ideal temp. scale is equal to the scale based on the perfect gas thermometer.

Example 5.2

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Carnot Cycle for Perfect Gas.

• Carnot cycle for a perfect gas is shown on T-S diagram.

• Pressure of gas changes from P4 to P1 during the isothermal heat supply.

• From P2 to P3 the isothermal heat rejection

9Fig 3: Carnot cycle for a perfect gas on a T-s diagram

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Fig 4: Carnot cycle on a P-v diagram

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In this cycle the heat supply & heat rejection processes occur reversibily at constant pressure.

The expansion and compression processes are isentropic.

The cycle is shown on a T-s diagram and a p-v diagram in Fig. 5.

The working substance is air, neglecting velocity changes, & applying the steady flow energy equation to each part of the cycle, we have;

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The constant pressure cycle

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Fig 5: (a) Constant pressure cycle on a P-v diagram & T-s diagram

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The constant pressure cycle (cont’d)

Fig 6: Closed-cycle gas turbine unit

As

=

Now since processes 1 to 2 & 3 to 4 are isentropic between the same pressure P2 and p1, then we have:

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The constant pressure cycle (cont’d)

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Hence putting in the expression for the efficiency;

Thus for the constant pressure cycle the cycle efficiency depends only on the pressure ratio.

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The constant pressure cycle (cont’d)

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The constant pressure cycle (cont’d)

Example 5.3

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The Otto Cycle

The Otto cycle is the ideal air standard cycle for the petrol engine, the gas engine and the high-speed oil engine.

The cycle is shown on a p-v diagram in Fig. 7

• Process 1 to 2 is isentropic compression.

• Process 2 to 3 is reversible constant volume heating.

• Process 3 to 4 is isentropic expansion.

• Process 4 to 1 is reversible constant volume cooling.

Efficiency is given by:

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Fig 7: Otto cycle on a p-v diagram

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Compression ratio = v1/v2.

The Processes 1 to 2 and 3 to 4 are isentropic and therefore there is no heat flow during these processes. Therefore

Example 5.4

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The Otto Cycle (cont’d)

The engines in use today which are called diesel engines are far removed from the original engine invented by Diesel in 1892.

Diesel worked on the idea of spontaneous ignition of powered coal, which was blasted into the cylinder by compressed air.

Oil became the accepted fuel used in compression-ignition engines.

Compression ration is given by, r = v1/v2

In Fig. 8

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The Diesel Cycle

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Fig 8: Diesel cycle on a p-v diagram

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The Diesel Cycle (cont’d)

Example 5.5

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The ideal cycle used as a basis for compression is called the dual-combustion cycle or the mixed cycle.

In Fig 9:

For heat added at constant volume & constant pressure respectively,

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The Dual Combustion Cycle

Example 5.6

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Fig 9: Dual-combustion cycle on a p-v diagram

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Reading AssignmentMean effective pressure

The Stirling Ericsson cycles

Example 5.7

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Questions ?

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