3.2_Energy Transfer by Heat and Work

CHAPTER 3.2 ENERGY TRANSFER BY HEAT AND

WORK

(2.4, 2.5, 4.1)

Lecture

Date:

3/22/2015 Thermodynamics I 1

2.4 Energy Transfer by Work


Work, like heat, is an energy interaction between a system and its surroundings.

As mentioned earlier, energy can cross the boundary of a closed system in the form of heat or work.

Therefore, if the energy crossing the boundary of a closed system is not heat, it must be work.

Heat is easy to recognize: Its driving force is a temperature difference between the system and its surroundings.

Then we can simply say that an energy interaction that is not caused by a temperature difference between a system and its surroundings

is work.

Work is the energy transfer associated with a force acting through a distance.



Work Done Per Unit Mass

Work is also a form of energy transferred like heat and, therefore, has energy units such as kJ.

The work done during a process between states 1 and 2 is denoted by W12, or simply W.

The work done per unit mass of a system is denoted by w and is expressed as

The work done per unit time is called power and is denoted W.

The unit of power is kJ/s, or kW.



Sign Convention for Work

(W > 0): Work is done by the system

(W < 0): Work is done on the system



Similarity Between Heat and Work

Heat and work are energy transfer mechanisms between a system and

its surroundings, and there are many similarities between them:



Differential for Point Functions and State Functions

Point functions (i.e., they depend on the state only, and not on how a

system reaches that state), and they have exact differentials designated

by the symbol d.

A small change in volume, for example, is represented by dV,

Path functions have inexact differentials designated by the symbol .

Therefore, a differential amount of heat or work is represented by Q

or W, respectively, instead of dQ or dW.



Electrical Work

In an electric field, electrons in a wire move under the effect of

electromotive forces, doing work.

When N coulombs of electrical charge move

through a potential difference V, the electrical

work done is

which can also be expressed in the rate form as

where,

V : Voltage, Volt

I : Current, Ampere



Electrical Work

In general, both V and I vary with time, and the electrical work done

during a time interval t is expressed as



Mechanical Work

There are several different ways of doing work, each in some way

related to a force acting through a distance.

The work done by a constant force F on a body displaced a distance s

in the direction of the force is given by:

If the force F is not constant, the work done is obtained by adding (i.e.,

integrating) the differential amounts of work,

The work done on a system by an external force acting in the direction

of motion is negative, and work done by a system against an external

force acting in the opposite direction to motion is positive.



Mechanical Work

1. Gravitational Work

2. Acceleration Work

3. Shaft Work

4. Spring Work

5. Moving Boundary Work

@ Constant Volume, @ Constant Pressure, @ Constant Temperature

Polytropic Process



1. Gravitational Work

Work required to move an object against force of gravity.

W = F ds

where F = mg and s = z

Therefore,

Wg = mg.dz z: elevation

Wg = mg (z2 z1) = PE2 PE1 ( z2 > z1)

Example 2-8



2. Acceleration Work

When a body is raised in a gravitational field, its potential energy

increases. Likewise, when a body is accelerated, its kinetic energy

increases.

Wa = m (v22 v1

2)/2 = KE2 KE1 (v2 > v1)

Example 2-9



3. Shaft Work

Energy transmission with a rotating shaft is very common in

engineering practice.

The power transmitted through the shaft is the shaft work done per unit

time, which can be expressed as

n = number of revoultions per unit time

T = torque

Example 2-7



4. Spring Work

Work involved in elongating or compressing a spring from rest

position.

W = F ds

Since F = k x for a linear spring

Take s = x or ds = dx

Therefore,

4.1 Moving Boundary Work


One form of mechanical work frequently encountered in practice is

associated with the expansion or compression of a gas in a piston

cylinder device.

During this process, part of the boundary (the inner face of the piston)

moves back and forth.

Therefore, the expansion and compression work is often called moving

boundary work, or simply boundary work (Fig. 41).

Gas

s s ds s1 s2



The total boundary work done during the entire process as the piston

moves is obtained by adding all the differential works from the initial

state to the final state:

This integral can be evaluated only

if we know the functional

relationship between P and V

during the process. That is, P = f

(V) should be available.



The area under the process curve on a P-V

diagram represents the boundary work.

2

1P dV WbArea

P

1 2

Process



A gas can follow several different paths as

it expands from state 1 to state 2.

In general, each path will have a different

area underneath it, and since this area

represents the magnitude of the work, the

work done will be different for each

process.

This is expected, since work is a path

function (i.e., it depends on the path

followed as well as the end states).



Constant Volume Process:

@ Constant volume:

Wb = P dV

Therefore,

Wb = 0 at constant volume

if V = constant, then dV = 0



Constant Pressure Process:

@ Constant Pressure (P = Po = constant )

Wb = P dV

Then,

Wb = Po (V2 V1)

= Po V



Expansion of gas against spring:



Constant Temperature:

Case 1: For an in Ideal gas law in a closed system



Constant Temperature:

Case 1: For systems involving liquids or phase changes

PROCEDURE:

1. Define phases of initial and final

states

2. Obtain properties of initial and

final phases as well as saturation

conditions

3. Draw the process path on a P-v

diagram (see the figure)

4. Calculate the area under the curve

(rectangles, trapezoids, etc.) v

T

const.

P



Adiabatic Process:



Polytropic process:



Polytropic process:

During actual expansion and compression processes of gases,

pressure and volume are often related by PVn = C, where n and C are

constants.



Polytropic process:

How to find the exponent n ----

Method 1: by plotting data

By plotting ln(P) vs ln(V) intercept = ln(C); slope = n

Method 2: From two data points

Example


SOLUTION:

Assuming Ideal Gas Behavior

Example


Since we have a polytropic process:

3.2_Energy Transfer by Heat and Work

Documents

Transcript of 3.2_Energy Transfer by Heat and Work