Work can be converted to heat directly and completely, but converting heat to work requires the use of some special devices. These devices are called heat engines.

HEAT ENGINES

Heat engines differ considerably from one another, but all can be characterized by the following:1. They receive heat from a high-temperature source (solar energy, oil furnace, nuclear reactor, etc.).2. They convert part of this heat to work (usually in the form of a rotating shaft).3. They reject the remaining waste heat to a low-temperature sink (the atmosphere, rivers, etc.).4. They operate on a cycle.

Heat EnginesDevices or machines that produce work from heat in a cyclic process. An example is a steam power plant in which the working fluid (steam) periodically returns to its original state.In such a power plant the cycle consists of the following steps:

Heat reservoirsBodies imagined capable of absorbing or rejecting an infinite quantity of heat without temperature change.

In operation, the working fluid of a heat engine absorbs heat IQHI from a hot reservoir, produces a net amount of work IWI, discards heat IQcI to a cold reservoir, and returns to its initial state. The first law therefore reduces to:

The thermal efficiency of the engine is defined as: η = net work output/heat absorbed

η = 1 – Tc/TH

For η to be unity (100% thermal efficiency), I Qc I must be zero. No engine has ever been built for which this is true; some heat is always rejected to the cold reservoir.

If a thermal efficiency of 100% is not possible for heat engines, what then determines the upper limit? One would certainly expect the thermal efficiency of a heat engine to depend on the degree of reversibility of its operation. Indeed, a heat engine operating in a completely reversible manner is very special, and is called a Carnot engine.

THE CARNOT CYCLE

•Reversible Isothermal Expansion (process 1-2, TH constant)•Reversible Adiabatic Expansion (process 2-3, temperature drops from TH to TL).•Reversible Isothermal Compression (process 3-4, TL constant).•Reversible Adiabatic Compression (process 4-1, temperature rises from TL to TH).

THE CARNOT VAPOR CYCLE•Consider a steady-flow Carnot cycle executed within the saturation dome of a pure substance.

•The fluid is heated reversibly and isothermally in a boiler (process 1-2)

•Expanded isentropically in a turbine (process 2-3)

•Condensed reversibly and isothermally in a condenser(partial) (process 3-4)

•Compressed isentropically by a compressor to the initial state (process 4-1).

Several impracticalities are associated with this cycle:

1.Limiting the heat transfer processes to two-phase systems severely limits the maximum temperature that can be used in the cycle (it has to remain under the critical-point value, which is 374°C for water).

Limiting the maximum temperature in the cycle also limits the thermal efficiency.

2.During isentropic expansion process (process 2-3) , the quality of the steam decreases. Thus the turbine has to handle steam with low quality, that is, steam with a high moisture content.

The impingement of liquid droplets on the turbine blades causes erosion and is a major source of wear.

Thus steam with qualities less than about 90 percent cannot be tolerated in the operation of power plants.

3. The isentropic compression process (process 4-1) involves the compression of a liquid–vapor mixture to a saturated liquid. There are two difficulties associated with this process.

First, it is not easy to control the condensation process so precisely as to end up with the desired quality at state 4. Second, it is not practical to design a compressor that handles two phases.

Some of these problems could be eliminated by executing the Carnot cycle in a different way. This cycle, however, presents other problems such as isentropic compression to extremely high pressures and isothermal heat transfer at variable pressures. Thus we conclude that

The Carnot cycle cannot be approximated in actual devices and is not a realistic model for vapor power cycles.

Many of the impracticalities associated with the Carnot cycle can be eliminated by:

Superheating the steam in the boiler andCondensing it completely in the condenser.

The cycle that results is the Rankine cycle, which is the ideal cycle for vapor power plants.

RANKINE CYCLE: THE IDEAL CYCLEFOR VAPOR POWER CYCLES

IDEAL RANKINE CYCLEThe ideal Rankine cycle consists of the following four processes:1-2 Isentropic compression in a pump2-3 Constant pressure heat addition in a boiler3-4 Isentropic expansion in a turbine4-1 Constant pressure heat rejection in a condenser

Energy Analysis of the Ideal Rankine Cycle

All four components associated with the Rankine cycle (the pump, boiler, turbine, and condenser) are steady-flow devices, and thus all four processes that make up the Rankine cycle can be analyzed as steady-flow processes.

The kinetic and potential energy changes of the steam are usually small relative to the work and heat transfer terms and are therefore usually neglected.

The steady-flow energy equation per unit mass of steam reduces to

The boiler and the condenser do not involve any work, and the pump and the turbine are assumed to be isentropic. Then the conservation of energy relation for each device can be expressed as follows:Pump ( q = 0) W pump, in = h2-h1

Boiler ( w = 0) q in = h3 – h2

Turbine ( q = 0) W turb, out = h3- h4

Condenser ( w = 0) qout = h4 – h1

The thermal efficiency of the Rankine cycle is determined from

Where

In areas where water is precious, the power plants are cooled by air instead of water. This method of cooling, which is also used in car engines, is called dry cooling.

Irreversibility is work required and work produced.Two steps are 2 to 3, and 4 to 1 These lines are no longer vertical but tend in direction of increasing entropy. Turbine exhaust is still wet, but as long as moisture contents is less than 10%, erosion problem are not serious. Slight sub cooling of the condensate in condenser may occur, but effect is inconsequential. The conversion efficiency of power plants in the United States is often expressed in terms of heat rate, which is the amount of heat supplied, in Btu’s, to generate 1 kWh of electricity.

BACK WORK RATIOAnother parameter used to describe power plant performance is the back work ratio, or bwr, defined as the ratio of the pump work input to the work developed by the turbine.