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ThermodynamicsChapter 4

Work and Heat

國立成功大學工程科學系

Work and heat are energy transfer from one system to another and thus play a crucial rolein most thermodynamic system on devices. As we want to analyze such systems, we need to model heat and work as functions of properties and parameters characteristic of the system or how they function.


Definition of Work


4.1

In elementary mechanics, the work done by a force F on a body displaced a distance inthe direction of the force is:

However, when treating thermodynamicsfrom a macroscopic point of view, it is advantageous to tie in the definition of work with the concepts of system, properties, and processes.


Work is done by a system if the sole effect on the surrounding could be the raising of a weight.

Work done by a system is positive; energy leaves the system.

Work done on a system is negative; energy is added to the system.

In general, work is a form of energy in transit, that is , energy being transferred across a system boundary.



Figure 4.1 Example of work crossing the boundary of a system.


Figure 4.2 Example of work crossing the boundary of a system because of a flow of an electric current across the system boundary.

Unit for Work


4.2

Raising of a weight

Work

Power


Shaft work

Specific work


Figure 4.3 Force acting at radius r gives a torque T = Fr.

Work Done at the Moving Boundary of a Simple Compressible System.


4.3

Considering Fig. 4.4 as a quasi-equilibrium process,


Figure 4.4 Example of work done at the moving boundary of a system in a quasi-equilibrium process.

Work done on the system during the process from state 1 to state 2

(∵ on ∴ is negative .)


Figure 4.5 Use of pressure-volume diagram to show work done at the moving boundary of a system in a quasi-equilibrium process.

Why the work done during each process is a path function (inexact differentials)not a point function (exact differentials)?

Figure 4.6 Various quasi-equilibrium processes between two given states, indicating that work is a path function.


Remarks:A work done during a process depends not only on the end states of the process but also on its path (e.g. the path from states “1” to “2” in Fig. 4.6) too.

A: The area underneath each curve in Fig. 4.6 represents the work for each process.

The differentials of point functions are exact differentials.

Thermodynamic properties are, of course, point functions.

The differential of path functions are inexact differentials


Two classes of problems:

1. on graphical form (e.g. experiments). Evaluate by graphical or numerical integration.

2. Analytical relations between P and V, e.g., polytrophic process: .


Remarks: Eqs. (4.5) or (4.6) are mathematical results, because there are cases in which work is not given by Eq. (4.4)! -- see Ex. 4.5.


Students read examples 4.1~4.5(Students read examples 3.1~3.7) -- recall


Other Systems That Involve Work


4.4

Consider as a system a stretched wire that is under a given tension. The work done by the system when the length of the wire is changed by an amount :

The minus sign above is due to work done by the system when is negativeSee Example 4.6Electric power is volts time ampere.

(Electric) power See P=Vi H.W#4.63, P88


Concluding Remarks Regarding Work


4.5

Work, in general, is given by the integral of the product of an intensive property (e.g. P) and the change of an extensive property(e.g. )


The identification of work in a process is an important aspect of many thermodynamic problems.

Q1: What is the work of the system comprising of both gas and vacuum shown below?

A: No work done because no work can be identified at the system boundary.


Figure 4.17 Example of process involving a change of volume for which the work is zero.

Q2: Work of the system comprising of the gas alone?

A: No work done in this processes of filling the vacuum, because 1. there is no resistance at the system boundary as V↑ 2. this is not a quasi-eq’m process, and therefore the work can not be calculated from .


Definition of Heat


4.6

Heat is defined as the form of energy that is transferred across the boundary of a system at a given temperature to another system (or the surroundings) at a lower temperature by virtue of the temperature difference between these two systems.


Another aspect of this definition of heat is that a body never contains heat. Rather, heat can be identified only as it crosses the boundary. Thus, heat is a transient phenomenon. Heat, like work, is a form of energy transfer to (positive) or from (negative) a system. The unit for it is the same as that for work.

SI unit for heat is Joule.


From a mathematical perspective, heat is a path function, and is an inexact differential

: heat transferred during the process from “1” to state “2”. Later, e.g. in Fig. 8.8 & 8.9

the rate of heat transfer

specific heat transfer


Heat Transfer Modes


4.7

Conduction: energy exchange between molecules. Energy is given out by molecules having more (energy) in the average (high temperature) to those having less (energy) in the average (low temperature).

This is Fourier law of conduction. The minus sign gives the direction of the heat transfer from a higher temperature to a low temperature.


Convection: the transfer of energy between a solid surface and the adjacent flowing fluid.

This is the Newton’s law of cooling.


Radiation: the transfer of energy due to the emission of electromagnetic waves in space (do not require any substances in space)


Comparisons of Heat and Work


4.8

Students read 4.8 and Summary


Figure 4.20 An example showing the difference between heat and work.


Chapter 4. Work and Heat.

Figure 4.7 Sketch for Example 4.1.


Figure 4.8 Pressure-volume diagram showing work done in the various processes of Example 4.1.


Figure 4.9 Sketch of physical system for Example 4.2.


Figure 4.14 Example of a nonequilibrium process.


Figure 4.18 Example showing how selection of the system determines whether work is involved in a process.


Figure 4.20 An example showing the difference between heat and work.


Figure 4.21 The effects of heat addition to a control volume that also can give out work.


【Homework Problems】

Figure P4.56

Chapter 3. Properties of a Pure Substance.

Figure 3.1 Constant-pressure change from liquid to vapor phase for a pure substance.

Chapter 3. Properties of a Pure Substance.

Figure 3.5 Pressure-temperature diagram for a substance such as water.

What processes (or cycles?)

什

麼

過

程

?

p = cV = c ?T = c

Q = 0也可能

Q ≠0

看懂題目的初始條件與過程 (變化) 條件，

配合查表或應用物質性質變化公式可知道物質(工作流體)的性質及其變化。對第四章言，主要計算功及工作流體的狀態變化。第五章則是應用1st Law…求(其中一個是第四章沒有計算的H.T.)系統之功、熱傳或性質的變化。

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