fundamentals of engineering thermodynamics chapter 9 questions

8/10/2019 Fundamentals of Engineering Thermodynamics Chapter 9 Questions

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Problems: Developir .;gineering Skills

571

Compressible

Flow

in

Nozzles and

Diffuse

rs

-

9.31) p 552

Momentum

equation for

steady state

one-dimensional flow

=

m(V2- V1

c = Vkii

M

=

V/c

h

0

=

h

+

V

2

/2

T

0

I

2

-=1 --M

9.37) p 554

9.38) p 554

9.39)

p

555

9.50)

p.

562

Ideal

gas

velocity of sound

Mach number

Stagnation enthalpy

Isentropic flow function relating

temperature

and

stagnation

temperature constant k

2

~ ~

= 1

M

2

T kl k- I) ( k _

l

l k- I )

9.51)

p

562

Isentropic flow function

relating

pressure

and

stagnation

pressure constant k

T

2

engines are said

to

produce higher torque than

gasoline engines. What does that mean?

2

Formula One race cars have 2.4 liter engines.

What

does

that signify? How is your car s engine sized in liters?

3

The ideal Brayton and Rankine cycles

are composed

of

the

same four processes, yet look different when represented on

a T-s

diagram

.

Explain.

4.

Th

e term regeneration is used to describe the use

of

regenerative

feedwater

heaters

in

vapor power plants

and

regenerative heat exchangers

in

gas

turbines

. In

what

ways

are

the purposes

of

these

devices simil

ar?

How do they differ?

5 You

jump

off

a raft

into the water

in the

middle

of a lake.

What direction does the raft move? Explain.

6 What

is the

purpose of a

rear diffuser

on a race

car?

7

What is the meaning

of

the octane rating that you see posted

on gas pumps? Why is it important to

co

ns

umers?

8

Why aren t jet engines of ai rliners fitted with screens to

avoid birds

being pulled into the intake?

9 When did the main power plant providing electricity

to

your

residence begin generating power? How long

is

it expected

to

continue operating?

10.

What

is the purpose

of

the gas turbine- powered auxiliary

power units

commonly seen at ai rp

orts

near

commercial

aircraft?

Otto, Diesel,

and Dual Cycles

9.1 An air-standard Otto cycle has a compression r

atio

of 9. At

the beginning of compression, p

1

= 100 kPa

an

d T

1

= 300 K.

The

heat

addition per unit

mass

of

air is 1350 kJ /kg.

Determine

(a) the net work, in kJ

per

kg of air.

(b)

the

thermal efficiency of the cycle.

(c)

the mean effective pressure, in kPa.

11. A nine-year-old

camper

is

suddenly awakened

by a

metallic click coming from the direction

of

a railroad track

passing

cl

ose to her campi

ng

area; soon afterward

, she

hears the

deep

growling

of

a diesel locomotive pulling an

approaching train. How would you interpret these diffe rent

sounds

to h

er?

12.

Automakers

have developed

prototype

gas

turbine

powered

vehicles, but

the

vehicles

have

not bee n generally

marketed to consumers. Why?

13. In

making

a quick stop at a friend s home, is it better

to

let your car s engine idle

or

turn it off and restart when you

leave?

14.

How

do today s more effective diesel engine exhaust

treatment systems work?

15.

What

is

the range of

fuel efficiencies, in miles

per

gallon,

yo u get wit h you car? At what speeds in miles per hour , is

the peak

achieved?

16. Where is Marcellus shale and why

is

it significant?

17 Does your state regulate the

practice

of

venting

high

pressure natural gas to

clean

debris from pipelines leading

to power plant gas turbines? What hazards are associated

with this practice?

(d) the maximum

temperature

in the cycle, in K.

(e) To investigate the effects

of

varying compression ratio,

n

plot each

of

the quantities calculated in parts (a) through IJiil..

(d)

for compression ratios ran

gi

ng from 1 to 12.

9.2

So lve Problem 9.1 on a cold air-standard basis with specific

heats evaluated

at

300 K.

9.3 At the beginning

of

the compression

process

of

an air

standard Otto cycle, p

1

= 1 bar, T

= 290 K, V

=

400

cm

3

•



I

57 Chapter 9 Gas Power Systems

The

maximum

temperature

in

the

cycle is 2200 K

and the

compression ratio

is 8.

Determin

e

(a) the

heat

addition, in kJ

(b) the

net

work, in kJ.

(c)

the

thermal efficiency.

(d) the mean effective pressure, in bar.

(e)

Develop

a full accounting

of the

exergy

transferred

to

the

air during

the heat

addition,

in

kJ

f)

Devise and evaluate an exergetic efficiency for the cycle.

Let T

=

290 K,

Po =

1 bar.

9.4 Plot each of the quantities specified in parts (a) through

(d) of Problem

9.3 versus

the compression ratio

ranging

from 2 to 12.

9.5 Solve

Problem

9.3 on a cold air-standard basis with specific

heats

evaluated at

300 K.

9.6 A four-cylinder, four-stroke

internal combustion engine

operates at

2800

RPM. The

processes within each cylinder

are modeled as an air-standard

Otto

cycle with a pressure

of

14 .7

lbf/in.

2

,

a

temperature of

80°

F, and

a volume

of

0.0196

ft

3

at the

beginning

of

compression.

The

compression ratio is

10,

and maximum pressure

in

the

cycle

is

1080 lbf in .

2

De t

e

rmine

, using a cold air-standard analysis with

k =

1.4,

the power developed by the engine, in horsepower, and the

m

ea

n effective pressure,

in

lbf/

in

.

2

9.7

An

air-standard

Otto

cycle has a compression ratio

of

8

and

the temperatur

e and pressure at the beginning of the

compression process are 520°R and 14 .2 lbf/in.

2

, respectively.

The

mass

of

air

is

0.0015

lb. The heat

addition

is

0.9 Btu.

De

termine

(a)

the

maximum

temperature,

in °R.

(b)

the

maximum pressure,

in

lbflin ?

(c)

the thermal

efficiency.

(d) To investigate

the

effects of varying compression ratio,

plot each of

the

quantities calculated in parts (a) through (c)

for compression ratios ranging from 2 to

12.

9.8

Solve

Problem

9.7

on

a cold air-standard basis with specific

heats evaluated at

520°R.

9.9

At the

beginning of

the

compression

proc

ess in an air

standard

Otto

cycle, p

1

=

14.7 lbf/in.

2

and

T

1

=

530°R. Plot

the thermal efficiency

and

mean effective pressure,

in

lbf in?,

for

maximum

cycle

temp

e

ratures ranging

from 2000

to

5000

°R

and com

pression ratios

of 6,

8,

and

10.

9.10 Solve

Problem

9.9 on a cold

air-standard

basis

using

k

= 1.4.

9.11 Consider

an

air-standard Otto

cycle.

Operating

data

at

principal

states in the

cycle

are

given in

the

table below.

The

states are numbered as in Fig. 9.3. The mass

of

air is 0.002

kg.

Determine

(a) the

heat

addition and the h

ea

t rejection, each in kJ.

(b) the

net

work,

in kJ

(c) the thermal efficiency.

(d) the mean

effective pressure,

in

kPa .

State T K)

kPa) kj/kg)

305 85

217.67

2

367-4

767·9

486.77

3

960

2006

725.02

4

458-7

127.8

329.01

9 U

Consider

a cold air-standard Otto cycle. Operating

data

at

principal

states in the

cycle

are

given in

the

table

below.

The states are numbered

as

in

Fig. 9.3.

The heat

rejection

from

the

cycle is 86

Btu

per lb of air. Assuming

c =

0.172 Btu/lb ·

0

R ,

det

e

rmine

(a)

the

compression ratio.

(b)

the net work per

unit mass

of

air, in Btu/lb.

(c) the thermal efficiency.

(d)

the mean

effective pressure,

in

lbf/in.

2

State

TC0R

lbf/in.

2

)

500

47-50

2

1204.1

1030

3

2408.2

2060

4

1000

95

9.13

Consider

a modification

of

the

air-standard

Otto

cycle

in

which the isentropic compression

and

expansion processes

are

each replaced with polytropic processes having

n = 1 3

The compression ratio is

9 for

the

modified cycle. At the

beginning of compression, p

1

= 1

bar and

T

1

= 300 K and

v =

2270 cm

3

. The

maximum

temperature

during

the cycle

is 2000

K. Determine

(a)

the heat transfer and work in

kJ, for each process in

the

modified cycle.

(b) the thermal efficiency.

(c)

the mean

effective pressure,

in

bar.

9.14 A four-cylinder, [our-stroke internal combustion engine

has a

bore

of 2.55 in .

and

a

stroke

of 2.10 in.

The

clearance

volume

is

12 of the

cy

lind

er volume at bottom dead

center

and the crankshaft rotates

at 3600

RPM. The

processes

within

each

cylinder

are modeled

as an air-standard

Otto

cycle with a pressure

of

14.6 lbf in.

2

and

a temperature of

l0 0°F at

the beginning

of

compression

. The maximum

temperature

in

the

cycle is 5200°R.

Based

on this

model,

calculate the

net work per cycle, in

Btu

,

and the power

developed

by

the

engine,

in

horsepower.

9.15 At the

beginning

of the

compression process

in an air-

r

standard

Otto

cycle, p

1

= 1 bar and T

1

= 300 K. The m x m u m



cycle

temperature is 2000 K. Plot the net work per unit

of

mass,

n

kJ kg, the thermal efficiency, and the mean effec

ti

ve

pr

essure,

n

bar, versus the compression ratio ranging from 2 to 14.

9 16

Investigate the effect

of

maximum cycle

temperature

on the

net

work

per

unit mass

of

air for air-standard

Otto

cycles with

compression ratios

of

5, 8,

and 11.

At

the

beginning

of

the

compression process, p

1

= 1

bar and

T

1

= 295 K.

Let the

maximum temperature

in

each case vary from 1000 to 2200 K.

9.17 The pressure-specific

volume

diagram

of the

air-standard

Lenoir cycle

is shown in

Fig. P9.17.

The

cycle consists of

constant volume heat addition isentropic expansion and

constant pressure compression.

For

the cycle, p

1

=

14.7 lbflin.

2

and

T

1

=

540°R.

The

mass

of

air

is

4.24

x

10-

3

lb,

and the

maximum

cycle temperature

is

1600

°R.

Assuming

c.=

0.171

Btu

/lb ·

0

R,

determine

for

the

cycle

(a) the

net

work , in Btu.

(b)

the

thermal

efficiency.

p

2

c

540°R

3

v Fig

P9 17

9.18 The pressure-specific volume diagram of

the

air-standard

Atkinson cycle

is

shown

in

Fig. P9.18.

The

cycle consists

of

isentropic

compression

,

constant volume heat addition

,

isentropic expansion,

and

constant pressure compression. For

a particular

Atkinson

cycle,

the compression

ratio

during

isentropic compression is 8.5 .

At

the beginning of this

compression process,p

1

=

100 kPa and T

1

=

300 K.The

constant

volume heat

addition per

unit mass of

air is

1400

kJ

/kg.

(a) Sketch the cycle on T s coordinates.

Determine

b)

the

net

work,

in

kJ

per

kg

of

air, c)

the thermal

efficiency

of

the cycle, and d)

the

mean effective pressure, in kPa.

p

3

2

4

v Fig P9 18

Problems:

Developing

Engineering

Skills

573

9.19

On

a cold air-standard basis, derive an expression for

the

thermal efficiency

of the

Atkinson cycle see Fig. P9.18)

in

terms

of

the volume ratio during the isentropic compression ,

the pressure ratio for the constant volume process, and the

specific

heat

ratio.

Compare the

thermal efficiencies

of

the

cold air-standard Atkinson and

Otto

cycles, each having the

same

compression ratio

and

maximum

temperature

. Discuss.

9.20 The

pressure and

temperature

at the beginning

of

compression

of

an air-standard Diesel cycle

are 95

kPa

and

300 K, respectively.

At

the end

of

the heat addition, the pressure

is

7.2

MPa and the

temperature

is

2150

K.

Determine

a) the compression ratio.

b)

the cutoff

ratio.

c)

the thermal

efficiency

of the

cycle.

d) the

mean

effective pressure, in kPa.

9.21 Solve

Problem

9.20

on

a cold

air-standard

basis with

specific heats

evaluated at

300 K.

9.22

Consider

an air-standard Diesel cycle.

At

the

beginning

of

compression , p

1

=

14.0 lbf/in.

2

and T

1

=

520°R. The mass

of

air

is

0.145 lb and the compression ratio

is

17.

The

maximum

temperature

in

the

cycle

is

4000°R.

Determine

a) the

heat

addition,

in

Btu.

b)

the thermal

efficiency.

c)

the cutoff

ratio.

9.23 Solve

Problem

9.22 on a cold air-standard basis with

specific heats

evaluated at

520°R.

9.24 Consider an air-standard Diesel cycle.

Operating

data at

principal

states in the

cycle

are

given

in the

table below.

The

states

are numbered

as

in

Fig. 9.5.

Determine

a)

the

cutoff ratio.

b)

the heat

addition

per

unit mass,

in

kJ/kg.

c)

the net work

per

unit mass,

in

kJ/kg.

d)

the thermal

efficiency.

State

T K) p kPa)

u kj/kg)

h

kj/kg)

1

380

100

271.69 380.77

2 1096.6

5197-6

842-40 1157-18

3

1864.2

5197-6 1548-47

2082.96

4

875-2

230.1

654-02

905.26

9.25 Consider a cold air-standard Diesel cycle.

Operating

data

at

principal

states in the

cycle

are

given

in the

table below.

The states are numbered

as in Fig. 9.5. For

k =

1.4, c

0.718 kJ / kg · K), and c

=

1.005 kJ/ kg · K),

determine

a)

the heat

transfer

per

unit mass and

work per unit

mass

for each process, in kJ/kg, and the cycle thermal efficiency.

b)

the

exergy transfers

accompanying heat and work

for

each process, in kJ/kg. Devise

and evaluate an

exergetic

efficiency for

the

cycle.

Let T

0

=

300 K

and p

0

=

100 kPa .

State

T K) p kPa) v

(m

3

/kg)

340

100

0.9758

2

1030-7

4850-3

0.06098

3

2061.4

4850·3

0.1220

4

897·3

263·9

0.9758

fundamentals of engineering thermodynamics chapter 9 questions

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