chapter 3 first law of thermodynamics and energy...

Prof. Siyoung Jeong

Thermodynamics I

MEE2022-02

Fundamentals of Thermodynamics

Chapter 3

First Law of Thermodynamics and

Energy Equation

Thermal Engineering Lab. 2

3.1 The energy equation

Chapter 3. First law of thermodynamics and energy equation



PEKEUE

EnergyPotentialEnergyKineticEnergyInternalE

mgzPEmVKE ,2

1 2

2 2

2 12 1 2 1 2 1

2

2 2

2 12 1 2 1 1 2 1 2

( )( )

2

2

( )( )

2

cv

cv

dE dU m d mgdz

m V VE E U U mg z z

mVdE dU d d mgz Q W

dEQ W

dt

m V VU U mg z z Q W

V V



2 1 2 2 2 1 1 1

2 2 2 1 1 1 1 2 1 2 1 2

( ) ( ) 0

( ) ( )

A B C A B C

A B C A B C A C B

m m m m m m m m

E E E E E E Q Q W


Ex. 3.1 A tank containing a fluid is stirred by a paddle wheel. The work input to

the paddle wheel is 5090 kJ. The heat transfer from the tank is 1500 kJ.

Consider the tank and the fluid inside a control surface and determine the

change in internal energy of this control mass.



3.2 The first law of thermodynamics


• For a control mass undergoing a cycle

WQ

WQJ



• For a change in state of a control mass

WQ

121 BA

1

2

2

1

1

2

2

1BABA WWQQ

1 2 1C B

2 1 2 1

1 2 1 2C B C BQ Q W W



1 1 1 1

2 2 2 2

1 1

2 2

A C A C

A A C C

Q Q W W

Q W Q W

Q W

depends only on the initial and final state not on the path.

122121 EEWQ

dEWQ


3.3 The definition of work


2

1

2

121 xdFdxFW

W = +: done by a system

W = - : done on a system

부호

[ / sec] [ ]

J N m

WW J W

dt



2 2 2

1 21 1 1

W F dx Frd Td

W F dx Frd Td

W dx dW F F V Fr T

dt dt dt

Ww

m


Ex. 3.2 A car of mass 1100 kg drives with a velocity such that it has a kinetic

energy of 400 kJ (see Fig. 3.6). Find the velocity. If the car is raised with

a crane, how high should it be lifted in the standard gravitational field to

have a potential energy that equals the kinetic energy?



Ex. 3.3 Consider a stone having a mass of 10 kg and a bucket containing 100 kg

of liquid water. Initially the stone is 10.2 m above the water, and the

stone and the water are at the same temperature, state 1. The stone then

falls into the water.

Determine ΔU, ΔKE, ΔPE, Q and W for the following changes of state,

assuming standard gravitational acceleration of 9.80665 m/s2.


a. The stone is about to enter the water, state 2.

b. The stone has just come to rest in the bucket, state 3.

c. Heat has been transferred to the surroundings in such an amount that

the stone and water are at the same temperature, T1, state 4.


3.4 Work done at the moving boundary of a simple compressible system


2

1

2

1

2

121 PdVPAdxdxFW

PAF

::

::

WdV

WdV


Ex. 3.4 Consider a slightly different piston/cylinder arrangement, as shown in

Fig. 3.10. In this example, the piston is loaded with a mass mp, the

outside atmosphere P0, a linear spring, and a single point force F1. The

piston traps the gas inside with a pressure P.



Ex. 3.5 Consider the system shown in Fig. 3.12, in which the piston of mass mp

is initially held in place by a pin. The gas inside the cylinder is initially at

pressure P1 and volume V1. When the pin is released, the external force

per unit area acting on the system (gas) boundary is comprised of two

parts :

Pext = Fext / A = P0 + mpg / A

Calculate the work done by the system when the piston has come to rest.




• Polytropic process work

2 2

1 21 1

2

1

2

1

21

1

1 1

2 1

1 11 12 1

1 1

1 1 1 2

1

1

1

( 1)

1

n

n

n

n n

nn n

n n

W W PdV

CdV

V

CV dV

VC

n

CV V

n

PVV V

n

PV V V

n

n

n

V

CP

CConstPV

.

n

VPVP

1

1122



n

P

PVP

n

P

PVP

n

V

VVP

n

n

n

n

n

1

1

1

1

1

1

1

1

211

11

1

211

1

1

211

n

n

nn

P

P

V

V

P

P

P

P

V

V

VPVP

1

1

2

1

2

1

1

2

2

1

1

2

2211



2

111

1

211

1

2

2

1

2

1

2

1

2211

ln

ln

ln

ln

.

P

PVP

V

VVP

V

VC

VC

dVV

CPdV

VPVPconstPV


Ex. 3.6 Consider as a system the gas in the cylinder shown in Fig. 3.14; the

cylinder is fitted with a piston on which a number of small weights are

placed. The initial pressure is 200 kPa, and the initial volume of the gas

is 0.04 m3.


a. Let the Bunsen burner be placed under the cylinder, and let

the volume of the gas increase to 0.1 m3 while the pressure

remains constant. Calculate the work done by the system

during this process.

b. Consider the same system and initial conditions, but at the

same time that the Bunsen burner is under the cylinder and

the piston is rising. Remove weights from the piston at

such a rate that, during the process, the temperature of the

gas remains constant. Calculate the work.


Ex. 3.6 (cont’d)


c. Consider the same system, but during the heat transfer

remove the weights at such a rate that the expression

PV1.3 = constant describes the relation between

pressure and volume during the process. Again, the

final volume is 0.1 m3. Calculate the work.

d. Consider the system and initial state given in the first

three examples, but let the piston be held by a pin so

that the volume remains constant. In addition, let heat

be transferred from the system until the pressure drops

to 100 kPa. Calculate the work.


3.5 Definition of heat


Heat : Temp. difference에 의해 전달되는 에너지

Sign +: to a system

-: from a system


3.6 Heat transfer modes


Conduction

Convection

Radiation

dx

dTkAQ

TAhQ

4

sATQ


Ex. 3.7 Consider the constant transfer of energy from a warm room at 20℃ inside a

house to the colder ambient temperature of -10℃ through a single-pane

window, as shown in Fig. 3.16.

The temperature variation with distance from the outside glass surface is

shown by an outside convection heat transfer layer, but no such layer is

inside the room (as a simplification). The glass pane has a thickness of 5 mm

(0.005 m) with a conductivity of 1.4 W/m∙K and . The outside wind is

blowing, so the convective heat transfer coefficient is 100 W/m2 ∙K. With an

outer glass surface temperature of 12.1℃, we would like to know the rate of

heat transfer in the glass and the convective layer.



3.7 Internal energy – a thermodynamic property


:

:

um

U

U

Intensive property

fgf

gf

ggff

vapliq

xuu

xuuxu

umummu

UUU

)1(

Extensive property


Ex. 3.8 Determine the missing property (P, T, or x) and v for water at each of the

following states:


a. T = 300℃, u = 2780 kJ/kg

b. P = 2000 kPa, u = 2000 kJ/kg


3.8 Problem analysis and solution technique


Ex. 3.9 A vessel having a volume of 5 m3 contains 0.05 m3 of saturated liquid

water and 4.95 m3 of saturated water vapor at 0.1 MPa. Heat is transferred

until the vessel is filled with saturated vapor. Determine the heat transfer

for this process.


Ex. 3.10 The piston/cylinder setup of Example 3.4 contains 0.5 kg of ammonia at -20 ℃

with a quality of 25%. The ammonia is now heated to +20 ℃, at which state the

volume is observed to be 1.41 times larger. Find the final pressure, the work the

ammonia produced, and the heat transfer.



Ex. 3.11 The piston/cylinder setup shown in Fig. 3.20 contains 0.1 kg of water at 1000

kPa, 500 ℃. The water is now cooled with a constant force on the piston until it

reaches half of the initial volume. After this, it cools to 25 ℃ while the piston is

against the stops. Find the final water pressure and the work and heat transfer in

the overall process, and show the process in a P-v diagram.



3.9 The thermodynamic property enthalpy


경우인 0, KEPEconstP

1 2 2 1 1 2

1 2 2 1

1 2 2 1 2 2 1 1

2 2 2 1 1 1

( )

( ) ( )

Q U U W

W P V V

Q U U PV PV

U PV U PV

Pvuh

PVUH

fgf

gf

xhhh

xhhxh

)1(


Ex. 3.12 A cylinder fitted with a piston has a volume of 0.1 m3 and contains 0.5 kg of

steam at 0.4 MPa. Heat is transferred to the steam until the temperature is

300 ℃, while the pressure remains constant. Determine the heat transfer and

the work for this process.



3.10 The constant-volume and constant-pressure specific heats


VdPdHQ

PdVdUWdUQ

PPP

P

vvv

v

T

h

T

H

mT

Q

mC

T

u

T

U

mT

Q

mC

11

11

CdTdudh

vdPduPvddudh

)(

Solid and Liquids


3.11 The internal energy, enthalpy, and specific heat of ideal gas


dvv

udT

T

udu

vTuuGenerally

Tv

),(



• Experiment of Gay-Lussac

12 2 1 12

2 1 2 2

1 1

2 1

( , ) ( )

( , ) ( ) 0

,

( , ) ( , )

0

g A B W

g A W

g A B g A

T

Q U U W

U U U T V V U T

U T V U T

T T

U T V V U T V

u

v

실험결과

dTmCdU

dTCdTT

udu

v

v

v

0



)(

)(

Tfh

RTTu

Pvuh

dTCdh

T

hC

P

P

P

0

RCC

RCC

RdTdTCC

RdTdudh

RTupvuh

vP

vP

vP

00

00

00 )(


Ex. 3.13 Calculate the change of enthalpy as 1 kg of oxygen is heated from 300 to

1500 K. Assume ideal gas behavior.



Ex. 3.14 A cylinder fitted with a piston has an initial volume of 0.1 m3 and contains

nitrogen at 150 kPa, 25 ℃. The piston is moved, compressing the nitrogen

until the pressure is 1 MPa. and the temperature is 150 ℃. During this

compression process heat is transferred from the nitrogen, and the work done

on the nitrogen is 20 kJ. Determine the amount of this heat transfer.



Ex. 3.15 A 25 kg cast-iron wood-burning stove, shown in Fig. 3.27, contains 5 kg of

soft pine wood and 1 kg of air. All the masses are at room temperature, 20 ℃,

and pressure, 101 kPa. The wood now burns and heats all the mass uniformly,

releasing 1500 W. Neglect any air flow and changes in mass and heat losses.

Find the rate of change of the temperature (dT/dt) and estimate the time it will

take to reach a temperature of 75 ℃.



3.12 General system that involve work


1. Wire

2. Surface Tension

dAW S

AEe

dLW

T


Ex. 3.16 During the charging of a storage battery, the current i is 20 A and the voltage

ε is 12.8 V. The rate of heat transfer from the battery is 10 W. At what rate is

the internal energy increasing?



3.13 Conservation of mass


2mcE

),( energyElightofvelocityc


Ex. 3.17 Consider 1 kg of water on a table at room conditions 20 ℃, 100 kPa. We want

to examine the energy changes for each of three processes: accelerate it from

rest to 10 m/s, raise it 10 m, and heat it 10 ℃.



3.14 Engineering applications



Homework Problems

2017: 42, 48, 60, 69, 75, 83,102, 111, 114, 132

2018: 42, 47, 63, 75, 81, 105, 111, 135


chapter 3 first law of thermodynamics and energy...

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