Chapter 22 Heat Engine, Entropy and the second law of thermodynamic

Chapter 22Heat Engine, Entropy and the second law of thermodynamic

Heat Engine and The Second Thermodynamic law

Heat Pumps & Refrigerators

The carnot Engine

Gasoline & Diesel Engine

Entropy

Entropy Changes in Irreversible Process

Entropy on a Microscopic Scale

Description Of Heat Engine

A heat Engine is a device that takes in energy by heat and operating in a cyclic process, expels a fraction of that energy by means of work.

22.1 Heat Engine and The second law of thermodynamic

A cyclic process of heat engine

When the engine absorb a quantity of energy(Qh) from the hot reservoir and then gives up a quantity of energy (QC) from cold reservoir

Through a cycle Eint = 0

From the firts law of thermodynamic

EInt = Q + w = Q-Weng

The net Weng done by a heat engine is equal to the net energy Qnet transferred to it.

Qnet = Qh - Qc ,therefore,

Weng=Qh - Qc

The Thermal Effeciency

Kelvin-Plank : its impossible to construct a heat engine that, operating in a cycle, produce no effect other than the input of energy by heat from a reservoir and performance of an equal amount of work.

Clausius : does not transfer energy doees not transferr spontaneously by heat from a cold object to a hot object

The Form of second law of thermodynamics

Quick quizz

22.1 (c). Equation 22.2 gives this result directly.

22.2 (b). The work represents one third of the input energy. The remainder, two thirds, must be expelled to the cold reservoir

Answer

Heat Pumps and Refrigerators is a device that transfer energy from cold reservoir to hot reservoir.

In a refrigerator or heat pump, the engine tahes in energy Qc from a cold reservoir and expels energy Qh from a hot reservoir.

Heat Pumps and Refrigerators

Coefficient of Performance

Quick Quiz

(d). The COP of 4.00 for the heat pump means that you are receiving four times as much energy as the energy entering by electrical transmission. With four times as much energy per unit of energy from electricity, you need only one fourth as much electricity.

answer

In the next section we discuss a theoretical heat engine that is the most efficient possible. To understand its nature, we must first examine the meaning of reversible and irreversible processes. In a reversible process, the system undergoing the process can be returned to its initial conditions along the same path on a PV diagram, and every point along this path is an equilibrium state. A process that does not satisfy these requirements is irreversible.

Reversible and Irreversible Processes

Although all real processes are irreversible, some are almost reversible. If a real process occurs very slowly such that the system is always very nearly in an equilibrium state, then the process can be approximated as being reversible. Suppose that a gas is compressed isothermally in a pistoncylinder arrangement in which the gas is in thermal contact with an energy reservoir, and we continuously transfer just enough energy from the gas to the reservoir during the process to keep the temperature constant. For example, imagine that the gas is compressed very slowly by dropping grains of sand onto a frictionless piston, as shown in Figure 22.9. As each grain lands on the piston and compresses the gas a bit, the system deviates from an equilibrium state, but is so close to one that it achieves a new equilibrium state in a relatively short time interval. Each grain added represents a change to a new equilibrium state but the differences between states are so small that we can approximate the entire process as occurring through continuous equilibrium states. We can reverse the process by slowly removing grains from the piston.

A general characteristic of a reversible process is that no dissipative effects (such as turbulence or friction) that convert mechanical energy to internal energy can be present. Such effects can be impossible to eliminate completely. Hence, it is not surprising that real processes in nature are irreversible.

The Carnot Engine

In 1824 a French engineer named Sadi Carnot described a theoretical engine, now called a Carnot engine, which is of great importance from both practical and theoretical viewpoints. He showed that a heat engine operating in an ideal, reversible cyclecalled a Carnot cyclebetween two energy reservoirs is the most efficient engine possible. Such an ideal engine establishes an upper limit on the efficiencies of all other engines. That is, the net work done by a working substance taken through the Carnot cycle is the greatest amount of work possible for a given amount of energy supplied to the substance at the higher temperature. Carnots theorem can be stated as follows

The net work done in this reversible, cyclic process because the change in internal energy is zero, the net work W engine done by the gas in one cycle equals the net energy transferred into the system, |Qh|-|Qc|. The thermal efficiency of the engine is given by Equation 22.2:

In Example 22.3, we show that for a Carnot cycle

Hence, the thermal efficiency of a Carnot engine is

Entropy Changes in Irreversible Processes

If the process is irreversible, then the total entropy of an isolated system always increases. In a reversible process, the total entropy of an isolated system remains constant.

The change in entropy of the Universe must be greater than zero for an irreversible process and equal to zero for a reversible process.

Entropy Change in Thermal Conduction

The energy transfer to or from each object is reversible, and we may set Q = Qr .

Because the cold reservoir absorbs energy Q, its entropy increases by Q/ Tc . At the same time, the hot reservoir loses energy Q, and so its entropy change is -Q/Th. Because Th > Tc , the increase in entropy of the cold reservoir is greater than the decrease in entropy of the hot reservoir. Therefore, the change in entropy of the system (and of the Universe) is greater than zero:

Entropy Change in a Free Expansion

Formula of the entropy change for the gas is

The isothermal, reversible expansion is only a replacement process that we use to calculate the entropy change for the gas; it is not the actual process.

The free expansion has no effect on the surroundings, and the entropy change of the surroundings is zero. Thus, the entropy change for the Universe is positive; this is consistent with the second law.

Entropy Change in Calorimetric Processes

Formula:

24

Gasoline and Diesel Engines

25

(Otto cycle)

Entropy

22.8 Entropy on a Microscopic Scale

In the kinetic theory of gases, gas molecules are represented as particles moving randomly.

Let us suppose that the gas is initially confined to a volume Vi , as shown in Figure 22.17a. When the partition separating Vi from a larger container is removed, the molecules eventually are distributed throughout the greater volume Vf (Fig.22.17b).

For a given uniform distribution of gas in the volume, there are a large number of equivalent microstates, and we can relate the entropy of the gas to the number of microstates corresponding to a given macrostate. The instant after the partition is removed (and before the molecules have had a chance to rush into the other half of the container), all the molecules are in the initial volume.

The ratio of the number of ways of placing the molecules in the volume for the initial and final configurations is

If we now take the natural logarithm of this equation and multiply by Boltzmanns constant, we find that

where we have used the equality N = nNA , that NAkB is

the universal gas constant R; thus, we can write this equation as

when n mol of a gas undergoes a free expansion

from Vi to Vf , the change in entropy is

we make the following important connection between entropy and the number of microstates for a given macrostate