Solution manual for thermodynamics for engineers 1st edition by kroos

1.3 D 1.4 B When the working fluid crosses the boundary, it is a control volume, as during intake and exhaust.. Temperature is the same for the entire room or half the room.. 1.15 B W

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1.1 (B) The utilization of energy is not of concern in our study If you use energy to power your car,

or your car seat is your own decision

1.2 (C) All properties are assumed to be uniformly distributed throughout the volume

1.3 (D)

1.4 (B) When the working fluid crosses the boundary, it is a control volume, as during intake and

exhaust The ice plus the water forms the system of (C) The entire atmosphere forms the

system of (D)

1.5 (C) An extensive property doubles if the mass doubles Temperature is the same for the entire

room or half the room

1.6 (D) A process may be very fast, humanly speaking, but molecules move very rapidly so an engine

operating at 4000 rpm is not thermodynamically fast All sudden expansion processes and combustion processes are non-equilibrium processes Air leaving a balloon is

thermodynamically slow

1.7 (B) If force, length, and time had been selected as the three primary dimensions, the newton would

have been selected and mass expressed in terms of the other three But, in Thermo-dynamics, the newton is expressed as kg·m/s2

1.8 (D) W = J/s = N ⋅ m/s = (kg ⋅ m/s2) ⋅ m/s = kg ⋅ m2/s3

1.9 (A) 34 000 000 000 N = 34 × 109 N = 34 GN (or 34 000 MN.)

V 8000×10 −6 m3

v = V =1 = 1 = 0.0008 m3/kg

ρ 1250 kg/m3

SG =

ρ

Hg =1250 kg/m3 = 1.25

ρ

1.11 (D) We must know if the surface is horizontal, vertical, on an angle? The surface cannot be

assumed to be horizontal just because it is drawn that way on the paper (Sometimes problems aren’t fair This is an example of such a problem.)

200 cm2 ×10−4

m2/cm2

A

1.13 (A) Use Eq 1.13 to convert to pascals:

p = ρ gH = (13.6 × 1000 kg/m3 ) × 9.81 m/s2 × 0.42 m

= 56 030 kg/m ⋅ s2 or 56.03×103 N/m2

1

1.14 (C) ∑ F = 0 PA + Kx = mg

P × π × 0.052 + 400× 0.2 = 40× 9.81. ∴ P = 39 780 N/m2 or 39.8 kPa gage The atmospheric pressure acts down on the top and up on the bottom of the cylinder and hence cancels out

1.15 (B) We do not sense the actual temperature but the temperature gradient between our skin and the

water As our skin heats up, the water feels cooler so we increase the water temperature until

it feels warm again This is done until out skin temperature ceases to change An object feels cool if its temperature is less than out skin temperature If that’s the case, a temperature difference occurs between our skin and the object over a very small distance,

creating a temperature gradient (Tskin−Tobject) / x .

1.16 (B) The energy equation states that at the position of maximum compression, the kinetic energy of

the vehicle will be zero and the potential energy of the spring will be maximum, that is,

1

2 m V2=1

2 Kx2 (The velocity must be expressed in m/s.)

1

× 2000

× K × 0.12.

∴ K = 98.8×106

N/m or 100

MN/m

2

× 3600

= 2

If the mass is in kg, the velocity in m/s, and x in meters, K will be in N/m But, check the

units to make sure

Get used to always using N, kg, m, and s and the units will work out You don’t have to always check all those units It takes time and on a multiple-choice test, there are usually problems left over when time runs out

1.17, 1.18, and 1.19. The Internet has the answers!

1.20 True Thermodynamics presents how energy is transferred, stored, and transformed from one

form to another If you use it to dry your hair, power your car, or store it in a battery, we

don’t really care Just use it any way that allows you to enjoy life!

1.21 Energy derived from coal is not sustainable since coal will eventually not be available,

even though that may take 500 years If an energy source is not available indefinitely, it is

not sustainable

1.22 Consult the Internet

1.23 A large number of engineers were required when the industrial revolution occurred

1.24 Trains were traveling the rails in the mid-1800s so mechanical engineers were needed, not

to drive the trains, but to design them! Coal was mined with a pick and shovel until the

late 1800’s Power plants and automobiles also came near the end of the 1800’s

1.25 It’s CO2 and it keeps things very cold Check it out on the Internet

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1.26 i) A system, ii) a control volume, iii) a system, iv) a system No fluid crosses the boundary of

a system Fluid crosses the boundary of a control volume

The system and

c.v are identical

Control surface

After

The system is the air inside plus that which has exited The c.v

extends to the exit of the balloon nozzle.

1.28 The number of molecules in a cubic meter of air at sea level is (3 × 1016 ) × 10 9 = 3 ×1025

V =

4

π r 3

=

1012 molecules

∴ r = 0.00002 m or 0.02 mm

1.29 Catsup is not a fluid It is a pseudo plastic or a shear-thinning liquid, whatever that is! A fluid

always moves if acted upon by a shear A plastic can resist a shear but then moves when the shear is sufficiently large Catsup is like that: first it won’t move, then it suddenly comes

1.30 From Wikipedia, 1 stone = 6.35 kg (= 14 lbm). ∴6.3 stones = 6.3× 6.35 = 40 kg

1.31 The units using Newton’s 2nd law are simpler:

lbf = slug × ft is simpler than lbf=lbm× 32.2 ft/s2

The conversion between mass and weight does not require the use of a gravitational constant when using the slug as the mass unit in the English system

1.32 Volume is extensive since it increases when the mass is increased, other properties remaining

constant

−1 % 0.001008

1.34 ρice = 1

= 1 = 57.2 lbm/ft3 ρwater = 62.4 lbm/ft3 So, ice is lighter than water at

0.01747

v

32ºF, so ice floats If ice was heavier than water, it would freeze from the bottom up That would

be rather disastrous Fish as well as skaters would have a problem You can speculate as to the consequences

3

1.35 SGHg = 13 600 = 13.6

1000

kg m

W = γ V = 13 600

×9.81

× 2 m3 =266 800 N

m 3 s 2 lbf W = 266 800 N × 0.2248 = 59,980 lbf

N 1.36 a ) ρ = 1 =1= 0.2 kg/m3, m = ρV = 0.2× 2 = 0.4 kg, W = mg = 0.4× 9.8 = 3.92 N v 5 b ) v =1 =1 = 0.5 m3 /kg, m = ρV = 2× 2 = 4 kg, W = mg = 4× 9.8 = 39.2 N 2 ρ c ) v = V= 2 = 0.002 m3 /kg, ρ = 1 = 500 kg/m3, W = mg = 1000× 9.8 = 9800 N

m 1000

0.002

d ) m = W = 1000= 102 kg, ρ = m =102= 51 kg/m3 , v = 1 =1 = 0.0196 m3 /kg

g 9.8

V 2

ρ 51

1.37 a ) ρ = 1 = 1 = 0.02 lbm/ft3 , m = ρV = 0.02× 20 = 0.4 lbm,

50 v

32.2 ft/s2

W = m g = 0.4 lbm ×

= 0.4 lbf

g c 32.2 ft-lbm/lbf-s2 b ) v =1 = 1 = 50 ft3 /lbm, m = ρV = 0.02× 20 = 0.4 lbm,

0.02 ρ

W = m g = 0.4 lbm × 32.2 ft/s2

= 0.4 lbf

g c

c ) W = m g = 1000 lbm × 32.2 ft/s2

=1000 lbf

g c 32.2 ft-lbm/lbf-s2

v = V = 20 = 0.02 ft3/lbm, ρ = 1 = 1 =50 lbm/ft3

1000 0.02 m v

d ) m = W g c = 500 lbf ×32.2 ft-lbm/lbf-s 2 = 500 lbm

g 32.2 ft/s2 v = V = 20 = 0.04 ft3 /lbm, ρ = 1 = 1 = 25 lbm/ft3

500 0.04 m v

This problem should demonstrate the difficulty using English units with lbm and lbf! Note that

lbm and lbf are numerically equal at sea level where g = 32.2 ft/s2, which will be true for

problems of interest in our study In space travel, g is not 32.2 ft/s2

1.38 ρ = 1

=1= 0.25 kg/m3, SG = ρ

x = 0.25 = 0.00025 , m = V = 8 m3 = 2 kg

W = mg = 2 kg × 9.81s m2 = 19.62 N (We used N = kg·m/s2.)

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1.39 v = 1 =

1

= 5 ft3 /lbm , SG =

ρx

=

0.2 lbm/ft3

= 0.00321

water 62.4 lbm/ft3

m = ρV = 0.2× 20 = 4 lbm, W = m g = 4 lbm × 32.2 ft/s

2

= 4 lbf

gc 32.2 ft-lbm/lbf-s2

1.40 Only (ii) can be considered a quasi-equilibrium process Process (i) uses a temperature

distribution in the room to move the heated air to other locations in the room, i.e., the temperature is not uniform When the membrane in process (iii) is removed, a sudden expansion

occurs, which cannot be considered a quasi-equilibrium process

1.41 From Table B-1 in the Appendix, we observe that So,

i) SG = 1.225 kg/m

3

= 0.001225

ii) SG = 0.6012×1.225 kg/m

3

= 0.000 736

iii) SG = 0.3376×1.225 kg/m

3

= 0.000 414

1.42 From Table B-1 in the Appendix, we observe find the local atmospheric pressure First,

P = 2.1 kg × 1002

cm2

× 9.81 m = 206 000 N/m2 or 206 kPa gage

(We used N = kg·m/s2.)

i) P = 206 kPa + 101 kPa = 307 kPa

ii) P = 206 kPa + 101× 0.887 kPa = 296 kPa

iii) P = 206 kPa + 101× 0.5334 kPa = 260 kPa

(We could have used Patm = 101.3 kPa or even 100 kPa since extreme accuracy is not of interest)

1.43 Refer to Fig 1.6 and Eq 1.14 The pressure in the tire would be P2 and P1 would be open to the

atmosphere:

P = 3 4 kg × 1002 cm 2 × 9.81m = 334 000kg ⋅ m/s2 = 334 000 N/m2 gage cm2 m2 s2 m2

1.44 P=ρ gh. 100 000 m2 = 786m3 × 9.81s2× h ∴ h = 13.0 m (We used N = kg·m/s )

= 1000 kPa ∴ P = 1000 kPa − 100 kPa = 900 kPa

5

1.46 P = ρ g h = 1000 kg × 9.81m× 0.25 m = 2453 Pa = 2.45 kPa gage

m3 s2

water

1.47 A measured pressure is a gage pressure.

P

abs

= P

gage

+ P

atm

b)P

abs= P

gage+ P

atm = 20 + 0.371× 14.7 = 25.45 psia or 3665 psfa

1.49 Consult the Internet

1.50 Consult the Internet

1.51 T ( °R ) = T( °F) + 460 = 120 + 460 = 580°R

1.52 T ( °C) = T(K) − 273 = 3 − 273 = −270°C

1.53 T ( °R) = T(° F) + 460 = 400 + 460 = 860°R

1.54 T (K) = 37 + 273 = 310 K

1.55 Use Eq 1.20:

a) R = R eβ(T0 −T )/T

0T

= 3000e4220(25 − 60)/ 298 ×333 = 677 Ω

0

b) R=R e β(T

0 −T )/T

0T

=3000e4220(25 −120)/ 298 ×393 = 97.8 Ω

0

c) R=R e β(T0 −T )/T

0T

=3000e4220(25 −180)/ 298 ×453 = 23.6 Ω

0

0.00018 2

H = 0.00018×

∴ H = 0.016 m or 16 mm

a) π

3 π × 0.003 × 20

4

0.000182

H = 0.00018×

∴ H = 0.032 m or 32 mm

b) π

π × 0.003 × 40

0.000182

H =

∴ H = 0.048 m or 48 mm

c) π 4 0.00018× 3 π × 0.003 × 60

1.57 V = 60 mi ×5280 ft/mi= 88 ft/s , KE = m V 2

hr 3600 s/hr 2gc

= 2500 lbm × 882 = 300,600 ft-lbf

× 32.2 ft-lbm/lbf-s2

6

or 300,600 ft-lbf

= 386 Btu

778 ft-lbf/Btu

The English unit on energy is most often the Btu (some authors use BTU)

2 m V 2 + mgh = 1

2 × 5000 × 802 + 5000 × 9.81× 1000 = 65× 106 N ⋅ m = 65 MJ

1.59 At 10 000 m, g=9.81−3.32×10−6

×10 000=9.777 m/s2

Wsurface = mg = 140 000 × 9.81 = 1.373×106 N

W10 km = mg = 140 000 × 9.777 = 1.369 ×106 N

140 000(9.81− 3.32 ×10−6

h ) dh

PE = ∫ mgdh = ∫

= 140 000 9.81× 10 000 − 3.32 × 10 −6 × 10 0002 = 1.373 10 10

× 10 − 0.0023×10

2

= 1.371× 1010 N ⋅

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