# Thermodynamics 題庫 What is the zeroth law of thermodynamics ...

Mechanics

Oct 27, 2013 (4 years and 8 months ago)

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Thermodynamics

1.

What is the zeroth law of thermodynamics?

2.

What is the difference between gage pressure and absolute pressure?

3.

The variation of pressure with density in a thick gas layer is given by
, where C
and n are constants. Noting that the pressure change across a differential fluid layer of
thickness
dz

in the vertical z
-
direction is given as
, obtain a relation for
pressure as a function of elevation
z
. Take the pressure and density at
z
=0 to be
P
0

and
, respectively.

4.

What are point and path function
s? Give some examples.

5.

A car is accelerated from rest to 85km/h in 10 seconds. Would the energy transferred to
the car be differen
t if it were accelerated to the sam
e speed in 5 seconds? Ignore

friction
and wind resistance.

6.

On a hot summer day, a student turns on his electric fan when he leaves his room in the
morning. When he returns in the evening, will the room be warmer or coole
r than the
neighboring rooms? Why? Assume all the do
ors and windows are kept closed.

7.

A classroom that normally contains 40 people is to be air
-
conditioned with window air
-
conditioning units of 5
-
kW cooling capacity. A person at rest may be assumed to
dissipate heat at a rate of about 360 kJ/h. There are 10 light bulbs in the room, each wit
h
a rating of 100 W.
The rate of heat transfer to the room through the walls and the
windows is estimated to be 15,000 kJ/h. If the room air is to be maintained at a constant
temperature of 21 degree, determine the number of window air
-
conditioning units
r
equired.

8.

Explain the following terms:(a) specific gravity, (b) state, (c) critical point, (d) quality, (e)
control mass.

9.

Calculate the gas pressure at D in the following diagram;
P
atm
=0.099M
Pa
, and the fluid
is mercury with a density of 13600kg/m
3
.

10.

A 75
-
hp (shaft output) motor that has an efficiency of 91.0 % is worn out and is to be
replaced by a high
-
efficiency motor that has an efficiency of 95.4 %.

The motor operates
4368 hours a year at a load factor of 0.75. Taking the cost of electricit
y to be \$0.08/kWh,
determine the amount of energy and money saved as a result of installing the high
-
efficiency motor instead of the standard motor. Also, determine the simple payback
period if the purchase prices of the standard and high
-
efficiency motors

are \$5449 and
\$5520, respectively.

11.

When a hydrocarbon fuel is burned, almost all of the carbon in the fuel burns completely
to form CO
2
, which is the principal gas causing the greenhouse effect and global
warming. On average, 0.59 kg of CO
2

is produced for each kWh of electricity generated
from a power plant that burns natural gas. A typical household refrigerator uses about
700 kWh of electricity per year. Determine the amount of CO
2

production that is due to
the r
efrigerators in a city wit
h 300
,000 households.

12.

Which process requires more energy:

completely vaporizing 1 kg of saturated liquid
water at 1 atm pressure or completely

vaporizing 1 kg of

saturated liquid water at 8 atm
pressure?

13.

Complete this table for H
2
O:

T (
0
C)

P (kPa)

v, m
3
/kg

Phase

50

7.72

400

Saturated vapor

250

500

110

350

50

cm

14.

One

kg of water fills a 150
-
L rigid container at an initial pressure of 2 MPa. The
container is then cooled to 40
0
C
. Determine the initial temperature and the final pressure
of the water.

15.

Explain why a large volume of steam ejecting from the pressure release valve of a
pressurized cooker when the value is opened. Plot the change of state of the water inside
the pressurized cooker on a P
-
T diagram before and after the valve is opened.

16.

Under
what conditions is the ideal
-
gas assumption suitable for real gases?

17.

A 0.09 m
3

container is filled with 0.9 kg of oxygen at a pressure of 600 kPa. What is the
temperature of the oxygen?

18.

A spherical balloon with a diameter of 9 m is filled with helium at 27

0
C and 200 kPa.
Determine the mole number and the mass of the helium in the balloon.

19.

A mass of 5 kg of saturated water vapor at 300 kPa is heated at constant pressure until the
temperature reaches 200
0
C. Calculate the work done by the steam during this
process.

20.

A mass of 2.4 kg of air at 150 kPa and 12
0
C is contained in a gas
-
tight, frictionless
piston
-
cylinder device. The air is now compressed to a final pressure of 600 kPa. During
the process, heat is transferred from the air such that the temperature

inside the cylinder
remains constant. Calculate the work input during this process.

21.

During some actual expansion and compression processes in a piston
-
cylinder device, the
gas has been observed to satisfy the relationship
, where

n

and
C

are constants.
Calculate the work done when a gas expands from 350 kPa and 0.03 m
3

to a final volume
of 0.2 m
3

for the case of
n
=1.5.

22.

An ideal gas contained in a piston
-
cylinder device undergoes an isothermal compression
process which begins with an initial pressure and volume of 100 kPa and 0.6 m
3
,
respectively. During the process there is a heat transfer of 60 kJ from the ideal gas to
the
surroundings. Determine the volume and pressure at the end of the process.

23.

-
flow compressor is used to compress helium from 100 kPa and 20
0
C at the inlet
to 1400 kPa and 315
0
C at the outlet. The outlet area and velocity are 0.001 m
2

and 30
m/
sec, respectively, and the inlet velocity is 15 m/sec. Determine the mass flow rate and
the inlet area.

24.

Steam flows steadily through an adiabatic turbine. The inlet conditions of the steam are 6
Mpa, 400
0
C, and 80 m/sec, and the exit conditions are 40 kPa
, 92 % quality, and 50
m/sec. The mass flow rate of the steam is 20 kg/sec. Determine (a) the change in kinetic
energy, (b) the power output, and (c) the turbine inlet area.

25.

A hot
-
water stream at 80
0
C

enters a mixing chamber with a mass flow rate of 0.5 kg/sec
where it is mixed with a stream of cold water at 20
0
C. If it is desired that the mixture
leave the chamber at 42
0
C, determine the mass flow rate of the cold
-
water stream.
Assume all stream are
at a pressure of 250 kPa.

26.

Argon steadily flows into a constant pressure heater at 300 K and 100 kPa with a mas
flow rate of 6.24 kg/sec. Heat transfer in the rate of 150 kW/sec is supplied to the argon
as it flows through the heater. (a) Determine the argo
n temperature at the heater exit, in
0
C.

(b) D
etermine the argon volume flow rate at the heater exit, in m
3
/sec.

27.

An ideal gas expands in an adiabatic turbine from 1200 K and 900 kPa to 700 K.
Determine the turbine inlet volume flow rate of the gas, in m
3
/sec, requiring to produce
turbine work output at the rate of 350 kW. The average values of the specific heats for
this gas over the temperature range and the gas constant are
c
p
=1.13 kJ/kg
-
K,
c
v
=0.83
kJ/kg
-
K, and R=0.30 kJ/kg
-
K.

28.

An automobile engine consu
mes fuel at a rate of 22 L/h and delivers 55 kW of power to
the wheels. If the fuel has a heating value of 44,000 kJ/kg and a density of 0.8 g/cm
3
,
determine the efficiency of this engine.

29.

An air conditioner produces a 2
-
kW cooling effect while rejecting
2.5 kW of heat. What
is its COP?

30.

An inventor claims to have devised a heat engine for use in space vehicles operating with
a nuclear
-
fuel
-
generated energy source whose temperature is 550 K and a sink at 300 K
that radiates waste heat to deep space. He also

claims that this engine produces 5 kW
while rejecting heat at a rate of 15,000 kJ/h. Is this claim valid?

31.

A homeowner is trying to decide between a high
-
efficiency natural gas furnace with an
efficiency of 97 % and a ground
-
source heat pump with a COP of

3.5. The unit costs of
electricity and natural gas are \$0.092/kWh and \$1.42/therm (1 therm = 105,500 kJ).
Determine which system will have a lower energy cost.

32.

A completely reversible heat pump produces heat at a rate of 300 kW to warm a house
maintained
at 24
0
C. The exterior air, which is at 7
0
C, serves as the source. Calculate the
rate of entropy change of the two reservoirs and determine if this heat pump satisfies the
second law according to the increase of entropy principle.

33.

Long cylindrical steel r
ods (
ρ
=7833 kg/m
3

and
c
p
=0.456 kJ/kg
-
K) of 10
-
cm diameter are
heat
-
treated by drawing them at a velocity of 3 m/min through a 6
-
m0long ovan
maintained at 900
0
C.
If the rods enter the oven at 30
0
C and leave at 700
0
C
, determine (a)
the rate of heat transfer to the rods in the oven and (b) the rate of exergy destruction
associated with this heat transfer process. Take T
0
=25
0
C.

34.

A wet cooling tower is to cool 40 kg/sec of water from 40 to 30
0
C. Atmosphere air
enters th
e tower at 1 atm with dry
-

and wet
-
bulb temperatures of 22 and 16
0
C,
respectively, and leaves at 32
0
C with relative humidity of 95 %. Using the psychrometric
chart, determine (a) the volume flow rate of air into the cooling tower and (b) the mass
flow ra
te of the required makeup water.

35.

Air enters a cooling section at 97 kPa, 35
0
C, and 30 % relative humidity at a rate of 6
m
3
/min, where it is cooled until the moisture in the air start condensing. Determine (a) the
temperature of the air at the exit and (b
) the rate of heat transfer in the cooling section.

36.

Determine the expansion process of the ideal Otto cycle, the gas is a mixture whose
volumetric composition is 30 % nitrogen, 10 % oxygen, 35 % water, and 25 % carbon
dioxide. Calculate
the thermal efficie
ncy of this cycle when the air at the beginning of the
compression is at 90 kPa and 15
0
C; the compression ratio is 8; and the maximum cycle
temperature is 1100
0
C. Model the heat addition and heat rejection process using constant
gas properties that are
the average of the air and expansion gas properties.

37.

Determine the change in the internal energy of helium, in kJ/kg, as it undergoes a change
of state from 100 kPa and 20
0
C to 600 kPa and 300
0
C using equation of state P(v
-
a)=RT
where a=0.01 m
3
/kg, and c
ompare the result to the value obtained by using the ideal gas
equation of state.

38.

A thermal
-
-
V car battery that draws 3 A of current
when running. The refrigerator resembles a small ice chest and is claimed to cool n
ine
canned drinks, 0.35 L each, from 25 to 3
0
C in 12 h. Determine the average COP of this
refrigerator.

39.

An air
-
standard cycle is executed within a closed piston
-
cylinder system and consists of
three processes as follows: 1
-

100 kPa and 27
0
C to 700
kPa. 2
-
3 Isothermal expansion until V
3

= 7 V
2
. 3
-
1 P=constant heat rejection to the initial
state. Assume air has constant properties with
c
v
=0.718 kJ/kg
-
K,
c
p
=1.005 kJ/kg
-
K,
R=0.278 kJ/kg
-
K, and
k
=1.4. (a)
Sketch the P
-
V and T
-
s
diagrams for the cycle. (b)
Determine the ratio of the compression work to expansion work. (c) Determine the cycle
thermal efficiency.

40.

A simple ideal Brayton cycle
uses helium as the working fluid; operates with 83 kPa and
15
0
C at the compressor inlet; ha
s a pressure ratio of 14; and a maximum cycle
temperature of 700
0
C. How much power will this cycle produce when the rate at which
the helium is circulated about the cycle is 50 kg/min? Use constant specific heats as the
room temperature.