Heat Transfer by Abhijit Debnath

CHAPTER

Selected Definitions Heat transfer: It is the process of transferring heat from an object at high temperature to an object at a lower temperature. Conduction: It is the process of transfer of heat between two substances that are in physical contact without mixing. Convection: It is the process of transfer of thermal energy from hot places to cold places by mixing of warmer portion with cooler portion of same material. Radiation: It is the process of transmission of heat through the empty space by electromagnetic radiation. Fourier's Law of beat transfer: This law states that rate of heat flow through a uniform material is proportional to the area (m2) and the temperature difference while it is inversely proportional to the length of path of the flow(m). Forced convection: If the mixing of fluid is accomplished by use of agitator or stirrer. Such a process in heat transfer is known as forced convection Natural convection: When a body of fluid is heated then mixing of fluid is accomplished by currents set up. Black body: It is a body that radiate maximum amount of energy at given temperature. Emissivity: It is defmed as ratio of energy emitted by actual body to energy emitted by black body. Absorptivity:

It is fraction of energy absorbed

Grey body: It is a body whose absorptivity remain constant at a given temperature at all wavelength of radiation. Heat excbangers: These are the devices used to transfer heat from hot gas to liquid through metal wall. Heat Intercbangers: wall.

These devices are used to transfer heat from one liquid to other liquid or one gas to other gas via metal

Bames: These are circular discs of metal sheet having perforated sheet on one side to receive tubes

4.1 INTRODUCTION All matter is composed of molecules and atoms. These atoms are always in different types of movement (translation, rotation or vibration). The movement of atoms and molecules produce heat or thermal energy. The more atoms or molecules move, the more heat or thermal energy they will have. Heat transfer include transferring heat from an object at high temperature to an object at a lower temperature. The main objectives of heat transfer process:

Heat Transfer

1. 2. 3. 4.

To To To To

study different mode of heat transfer determine the rate of heating and cooling plan changes in new heat transfer equipments determine the efficiency of existing heat exchange equipments.

4.2 APPLICATIONS 1. Heat is required for drying of wet mass during production of tablet. 2. During distillation, heat is required to convert liquid into vapor. Therefore individual component get condensed at other place, 3. In case of steam distillation, steam is required which is in direct contact with material 4. To prepare vegetable extract by process of evaporation, heat is supplied to liquid. Therefore vapors are formed which are removed. 5. For crystallization of drugs, supersaturation is achieved by heating saturated solution. 6. For sterilization of pharmaceuticals, dry heat is required for sterilization of glasswares and containers while steam is required for autoclaving. 7. For different processes such as boiling, fusion etc, heat is also required.

4.3 MECHANISM OF HEAT TRANSFER The heat can travel from one place to another in three ways: Conduction, convection and radiation. The heat will always find a way to transfer from the higher system to the lower system. Heat transfer is a dynamic process .

.3.1 CONDUCTION Conduction is the transfer of heat between two substances that are in physical contact without mixing. The better the conductor, the sooner the heat will be transferred. The metal is a good conductor of heat. Conduction occurs when a substance is heated, the particles acquire more energy and vibrate more. These molecules then bump into the neighbouring particles and transfer some of their energy to them. It then continues and transmits the energy from the hot end to the most to the colder end of the substance.

4.3.2 CONVECTION In convection, thermal energy is transferred from hot places to cold places by mixing of warmer portion with cooler portion of same material. For example water boiling in a pan. Another good example of convectiorris in the atmosphere. The surface of the earth is heated by the sun, warm air rises and cool air enters. If motion of fluid is due to difference in density which occur by difference in temperature, then it is called natural convection. If motion of fluid is due to mechanical mean, then it is called forced convection.

4.3.3 RADIATION Radiation is a method of heat transfer that does not related to any contact between the heat source and the heated object, as in the case of conduction and convection. The heat can be transmitted through the empty pace by electromagnetic radiation. This process of energy transfer is known as radiation. Examples of radiation are the heat of the sun or the heat generated by the filament of a bulb.

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4.4 HEAT TRANSFER BY CONDUCTION Heat flow when there is temperature gradient. If one end of a metal rod is at a higher temperature, then the energy will be transferred down towards the cold end. The higher velocity particles collide with the slower particles with a net transfer of energy to the slower particles.

Figure 4.1: Mechanism of heat transfer The basic rate equation is Rate

= driving

force / resistance

The driving force is temperature drop across the solid surface. Greater will be rate of heat flow if temperature drop is greater. The term resistance is expressed by Fourier's Law

dL t1

~-----,l Figure 4.2: Heat transfer through metal wall by conduction If heat is transferred through a metal wall having area A and thickness L. Let t, is higher temperature uniform on the one face of the wall while t2 is uniform but lower temperature maintained on the another face of wall. The flow will be from higher temperature side to lower temperature side. Fourier's Law state that rate of heat flow through a uniform material is proportional to the area (m2) and the temperature difference while it is inversely proportional to the length of path ofÂˇthe flow(m).

Rate of heat flow

Area x Temperature

a ------------'-~

difference

Thickness

(~t ) (4.1)

Heat Transfer

A.~t

qa--

KmÂˇA.~t

(4.2) (4.3)

Where Km is mean proportionality constant If heat flow is at right angle to plane A and suppose to be in steady state. Consider at an intermediate point in the wall having thickness dL of a thin section. This is parallel to plane A. Fourier law for this thin section is shown as

dQ de

-K.A.dt dL

(4.4)

here Q= heat transfer 8

= time = proportionality constant. It is function of temperature and independent on length

dt / dL= temperature gradient egative or minus (-) sign indicate decrease in temperature in the direction of flow. For steady state heat transfer, equation will become

dQ -K.A.dt - = constant = q = --de dL q.dL =-kdt A

(4.5)

(4.6)

integrating the above equation between 0 to L L

qJ o

dL =-

Jkdt= It

Jkdt

(4.7)

qL / A = km (tl-t2) = km~t

(4.8)

is arithmetic mean value of k between temperature tl and t2 and considered as constant. In teady state heat transfer q remain constant. The term ~t indicates driving force. The equation (4.3) will

(4.9)

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(4.10)

Resistance = L / kmA

Fourier's law describe resistance in quantitative way.

4.5 FLOW OF HEAT THROUGH COMPOUND RESISTANCE IN SERIES

Lower temperature side

~LI

:"2

Higher temperature side

L3~

Figure 4.3: Flow of heat through compound resistance in Series Suppose a flat wall made of series of layer having thickness of three layers are L" ~, L3 and conductivities k., k2, k3. The area of entire wall is A. Temperature drop across three layers is M,. ~t2. ~t3. The Resistance of three layers R" R2,R3. If ~t is overall temperature drop over the three layers, then ~t = ~t,

+ ~t2 + ~t3

~t, = q.. L,/ k, A and ~t2 = q2. ~/ k2 A and ~t3= q3. Ly k3 A

(4.11)

The entire heat must pass from first resistance also pass from second and third. So heat q is q = q, + q2 + q,

(4.12)

(4.13)

(4.14)

Heat Transfer

When heat flow through number of resistances in series, the temperature difference are total temperature drop and individual thermal resistance is to the total thermal resistance expressed mathematically as (4.15)

4.6 HEAT FLOW THROUGH THICK WALL CYLINDER

Figure 4.4: Heat flow through thick wall cylinder

Consider a hollow cylinder having rl. r2 and r is radius of inner wall, radius of outer wall and radius of thin cylinder respectively. tl is temperature of inside surface (higher) and t2 is temperature of outside surface (lower). dr is thickness of thin section. N is the length of hollow cylinder. Km is mean thermal conductivity of material of cylinder. The rate of heat transfer is expressed as

dt q =-k-(27trN) dr

(4.16)

where A = 2mN and dl, = dr On rearranging the equation by considering variables radius and temperature

dr / r =

-21tNk

(4.17)

Integrating the above equation f2

J dr / r = -21tN rJ

(4.18)

In r2 - In rl

27tNKm q

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(tl - t2 )

Engineering

(4.19)

27tNKm (tl - t2 ) q = --,:::-...:...-'--:-~ In(r2/rl)

(4.20)

Comparing this equation with general form (4.21)

Here Am is heat transfer area of cylinder having length N and radius rm. And L = r2- rl.

27tN( r

2 l =--:....::...----'-'m

In(r2/rl)

(4.22)

(4.23) Hence Where rm is logarithm mean radius. It is used to calculate heat flow in case of thick walled tube. The arithmetic mean radius tr, + r2) /2 provide value within 10% of rmif r2/rl is less than 3.2. Its value will be 1% ifr2/r1 is less than 1.5.

4.7 HEAT TRANSFER BY CONVECTION When a body of fluid is heated then mixing of fluid is accomplished by currents set up. This is called natural convection. If the mixing of fluid is accomplished by use of agitator or stirrer. Such a process in heat transfer is known as forced convection. The flow of fluid flow through pipeline can be either viscous or turbulent in nature. When fluid follows viscous flow, the velocity is zero at actual surface of wall. The layer of fluid adjacent to wall act as stagnant film. Also in case of turbulent flow, stagnant film is observed. The fluid is in turbulent flow at the centre while viscous flow is observed at surface of fluid. A film of buffer layer exist between these type of flow. The resistance offered by these films for flow of heat is large because these films are thin. Beyond these films, turbulence cause rapid equalization of temperature.

Heat Transfer

4.8 TEMPERATURE GRADIENT IN FORCED CONVECTION C

Metal wall

Cold fluid

Warm fluid

H Figure 4.5: Temperature gradient in forced convection 'hen heat flow from hot fluid through metal wall into cold fluid through a metal wall. The dotted line on both side of metal represent boundaries of viscous film on hot and cold side respectively. The metal wall thickness is represented by L. The fluid to right of HR and left to CC are in turbulent flow. The temperature gradient ta is the maximum temperature in hot fluid. tb is the temperature at the boundary of warm side between turbulent and viscous flow junction. tc is temperature at actual interface between warm fluid and lid surface. Curve ta, tb, t, represent temperature gradient from bulk of warm fluid to metal wall. tl is -erage temperature on warm fluid side.t, is minimum temperature on cold fluid. 1" is temperature at '>Ynchr-v on cold side between turbulent and viscous flow junction. 41 is temperature at actual interface n cold fluid and solid. te is minimum temperature on the cold fluid. Curve 41, 1", tf represent ~::;:IC!ranlflegradient from bulk of cold fluid to metal wall. t2 is average temperature on cold fluid side. ult to estimate thermal resistance of fluid film. Because thickness of film cannot be determined

I:. Re istance offered by these film cannot be calculated separately. The thickness of film depend on nvection. So film coefficient is determined by indirect method. Suppose q watt of heat flow through uid to cold one and same amount of heat is passed through stagnant film on hot side, through metal through stagnant film on cold side. Let Al is area of metal on hot side. A2 is area of metal on cold average area of metal wall. On hot side, surface or film'coefficient hI is defined as (4.24)

:J:~a::c:;miÂˇlng this equation with (eq 4.8), it can be found that h, is analogus to k/L and l/h.A, is known as . ce. It is due to joined effect of viscous film HR and turbulent core that further lead to 'l::::p!:D::::re difference (ta-tb).

;pJ

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On cold side, surface or film coefficient hi is defmed as

(4.25) Ilh2A2 is known as thermal resistance

To determine overall heat transfer from IlhlAI thermal resistance on hot fluid side, Ilh2A2 is thermal resistance of cold fluid side and UkAm resistance of metal wall., the equation will be written as (4.26)

On multiplying both numerator and denominator of right side of equation by AI, we get

(4.27)

Then overall heat transfer V I is expressed as

(4.28)

The equation (4.27) can be written as q = VI LltAI The rate of heat transfer is product of overall heat transfer coefficient, temperature drop.

(4.29) area of heating surface

and

The overall heat transfer coefficient for tubular metal wall is (4.30)

When one particular area is more convenient than other. Let assume h2 is much greater than hi, then the (DI1D2h2) become small as compared to Ilhl. As well as resistance of tube wall is also small as compared to Ilhl. The ratio (DdDro> and (DdD2) can be disregarded. The equation will be

u = I

1 11 hi +L/k+lIh2

(4.31)

The equation is used in case of thin walled tube with larger diameter and also for thin walled plates. In these cases, area A can be used for AI. Am and A2. The error will be negligible. In these cases VI = V2=Vmâ&#x20AC;˘

Heat Transfer

When hi is very small as compared to h2 and (Uk), (llbl) will be larger. So other two terms in denominator are disregarded. Then VI =hl. The numerical value of surface coefficient can be predicted easily. When fluid pass through each other from the opposite directions, then this arrangement is called counter current or counter flow. In this case the exit temperature of hot fluid is less than that of exit temperature of cold fluid. Therefore a large proportion of heat content of hot fluid is extracted for given entrance temperature of cold fluid. If Lltl is nearly constant to Llt2, then Lltavcan be expressed as (eq 4.32)

For counter current heat flow, heat transfer equation is written as

q = VA.Llt.v

(eq 4.33)

4.9 RADIATION When above source follow

heat transfer occurs by the absolute zero emits for thermal radiations. same laws of light such

radiation, then it is called thermal radiation. All matter with a temperature thermal radiation. The wavelength of 0.8 to 400 urn are used as radiation The range is 0.8 to 25 urn are used for industrial use. Thermal radiations as it travels in straight line and it may be reflected from the surface.

Black body is a body that radiate maximum amount of energy at given temperature. For visible light rays black matte surface approaches a black body. Black surface emit more heat than polished surface. Theoretically an enclosed space with small opening is considered as black body and temperature in that enclosed space should be constant. The total amount of radiation emitted by black body is explained by Stefan-Boltzmann Law. According to this q = bAr

(eq 4.34)

here q = energy radiated in one second A = Area of radiating surface

= =

solute temperature of radiating surface t

For black body b = 5.67 X 10-8 W/m2 K4.

.5:!r,iII:=al body, the above equation is expressed as

(eq 4.35)

q=ebAr

~:ssiviry

of actual body.

E = 1. For actual body E is less than 1. Emissivity is defined as ratio of energy emitted by .:::::::'::!1XICY. to energy emitted by black body.

;:::so::r:;~iUy. . fraction of energy absorbed. The substance is considered as black body if E = :::ÂŁXi: ~xX!y' one, then Absorptivity must be one.

11.

If Emissivity

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Grey body is a body whose absorptivity remain constant at a given temperature at all wavelength of radiation. Suppose a small body having surface area A and temperature T 2 is surrounded by hot black bod at temperature T 1. The amount of heat transferred in such process is expressed by Stefan Law (eq 4.36)

4.10 HEAT EXCHANGERS AND HEAT INTERCHANGERS Heat exchangers are the devices that are used to transfer heat from hot gas to liquid through metal wall. Different types of heat exchangers are a.

Shell and tube heater

Multipass heater

Two pass floating head heater

4.10.1 Shell and tube heater It is single pass tubular heater. Steam inlet

Vent Cor non condensed gases

,1',

Liquid outlet

•

• • •

• •

Distribution chamber

Distribution chamber Liquid inlet

Condensate outlet

Figure 4.6: Single pass tubular heater Construction It consist of number of parallel tubes. The both end of the tubes are fitted into tube sheets. The tubes are enclosed in casing which is cylindrical in shape. Two distribution chambers are enclosed by cover Liquid inlet is provided to distribution chamber. There are also provision of steam inlet, condensate outlet and vent for non condensed gases.

Working Steam is introduced through inlet into the space around tubes. Therefore tubes get heated. Conde vapors and non condensed gases are escape through outlets provided. The liquid which is to be heated is pumped into I"t distributing chamber. The fluid in tubes get heated due to heat transfer by conducti

Heat Transfer

through metal wall, followed by stagnant layer and finally by convection. The hot liquid enters into 2nd distribution chamber and leaves through outlet. The advantage of this heat exchanger is that the large heating surface can be packed into small volume. But its disadvantage is the cross sectional area of ,tubes are large but velocity of fluid in the tubes are low. Therefore heat transfer coefficient is also low .

.10.2 Multipass heater The main advantage of Multipass heater is to improve velocity of fluid.

i I

c A

(iil?\

'lli7

Figure 4.7: Multipass beater Construction: It consist of number of parallel tubes. The end of the tubes are fitted into tube sheets. The tubes are enclosed in casing. Baffles are placed in distribution heads. There are also provision for entrance and exit of the fluids.

Working The feed is entered into the compartment A of one of the head. Then it is passed through tubes into compartment B of other head. Then fluid back through other set of tubes to compartment C of the first head and finally leaves through compartment I. The fluid is diverted by using baffles. Since heater is multipass, so same liquid has to flow through several tubes back and forth. The construction of heater is very complicated which is disadvantage of heater. Another disadvantage is multiple number of entry and exit points increase cost of pumping of fluid and also cause friction loss.

it!

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4.10.3 Two pass floating head heater Steam inlet ~

Vent

Liquid outlet

~~--------~I----~{~,---( Floating bead --1--/

l~E~;a;~;Ei~-t~ ~

Partition

Distribution cbamber Condensate outlet

Tubes Liquid inlet

Figure 4.8: Two pass floating head heater It consist of bundles of parallel tubes which are enclosed in casing. There are two distribution chambers and one of the distribution chamber is partitioned. The fluid inlet and outlet are also attached to same chamber. Other distribution chamber is like floating head. The end of tubes are embedded into floating head. There are also provision for steam inlet and outlet for non condensed vapors and condensate. The steam is passed through inlet. As a result tube get heated. The non condensed vapour pass through outlets. The fluid to be heated is introduced into one distribution chamber. From there fluid reaches to floating head, the direction of then fluid entered into second side of partition of distribution chamber. Due to liquid leaves through the outlet provided.

gases and condensed side of partition of fluid is changed and heated tubes, the hot

The floating head arrangement is advantageous because the tube sheet is structurally independent of the shell.

4.11 HEAT INTERCHANGERS These devices are used to transfer heat from one liquid to other liquid or one gas to other gas via metal wall.

4.11.1 Bames These are circular discs of metal sheet having perforated sheet on one side to receive tubes. The baffles are placed outside the tube to increase the path and decrease the cross section of the path of the second fluid. The baffles also increase the velocity of the liquids outside the tubes and also make the liquid to flow more or less perpendicular to the tubes. This produces additional turbulence which decreases the resistance to transfer for heat transfer outside the tubes.

Heat Transfer

4.11.2 Liquid to liquid interchangers: Spacer tubes Inlet cold liquid Outlet hot liquids -1-

Inlet hot liquid -1-

-+ Outlet heated liquid

Tubes Figure 4.9: Construction of liquid to liquid heat interchangers The apparatus consist of tube sheets, spacer rods and baffles. Tube sheets are attached by guide rods with set screws. Baffles are attached having perforations in which tubes are inserted. The whole assembly is enclosed in shell. There are also provision for hot liquid inlet and fluid outlet. Two distribution chambers are also present. In one distribution chamber there is inlet for cold liquid while in another distribution chamber there is outlet for heated liquid. The hot fluid is entered from inlet to the outside of tubes. The fluid changes the direction and rise again. Baffles allow flow of fluid to more or less right angle to tubes. As a result, the baffles get heated and further tubes also get heated. When cold liquid entered through inlet provided. It passes through tubes and also get heated. The heated liquid is collected from outlet provided in distribution chamber. The heat transfer is rapid in this case and liquid flow more or less right angle to tubes which is the advantage of liquid liquid heat interchangers.

4.11.3 Double pipe heat interchanger They often have a U-tube structure to accommodate thermal expansion of the tubes without necessitating expansion joints. A double pipe heat interchanger (also sometimes referred to as a 'pipe-in-pipe' interchanger) is a type of heat interchanger comprising a 'tube in tube' structure. As the name suggests, it consists of two pipes, one within the other. One fluid flows through the inner pipe whilst the other flows through the outer pipe, which surrounds the inner pipe. Counter current flow in these interchangers are used when very close temperature are required.

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Shell-side fluid in Flange Tube-side fluid out

Shell-side fluid out Figure 4.10: Double pipe heat interchangers

4.11.4 Finned tubes:

1.1. 1. 1. 1. 1. 1. 1.1.r

Fins

Tube

vvv

TTTTTTTTTT Rectangular fins Longitudinal fins

Spiral fins

Figure 4.11: Finned tubes The varieties of fins are available. Rectangular discs of metals may be placed at right angle to tubes. Spiral fins may be attached to tubes. Longitudinal fins are also used. Fins are used to decrease size of apparatus. They also increase rate of heat transfer. The air is present outside steam side surface is high overall coefficient is low. side. The surface area can

the tube while steam is present inside the tube. The heat transfer coefficient on but on air side it is low. So the overall coefficient is shift to air side. The value of The rate of heat transfer can only be increased by increasing surface area on air be enhanced by attaching fins to outside the tubes.

Heat Transfer

C)EVIEW 1.

QUESTIONS

Define Conduction. Answer- It is the transfer of heat between two substances that are in physical contact without mixing.

Define Convection Answer- It is the process of transfer of thermal energy from hot places to cold places by mixing of warmer portion with cooler portion of same material.

Define Radiation Answer- It is the process of transmission of heat through the empty space by electromagnetic radiation.

Deflae Grey body. Answer- It is a body whose Absorptivity remain constant at a given temperature at all wavelength of radiation.

Define Emissivity Answer- It is defined as ratio of energy emitted by actual body to energy emitted by black body.

HORT ANSWER OUESTIONS 1.

What are the mechanism of beat transfer? Answer- The heat can travel from one place to another in three ways: Conduction, convection and radiation. The heat will always find a way to transfer from the higher system to the lower system. Heat transfer is a dynamic process Explain Fourier's

Law of heat transfer.

Answer- Fourier's Law state that rate of heat flow through a uniform material is proportional to the area (m2) and the temperature difference while it is inversely proportional to the length of path of the flow(m). Rate of heat flow

area x Temperature difference (fit) I thickness

q Cl A. fit! L

KmÂˇA.L\t q = ---""----L

Define black body and explain Stefan BoItzmann's Law. Answer- Black body is a body that radiate maximum amount of energy at given temperature. For visible light rays black matte surface approaches a black body. Black surface emit more heat than polished surface. The total amount of radiation emitted by black body is explained by Stefan-Boltzmann Law. According to this q=bAr where q = energy radiated in one second A = Area of radiating surface T = absolute temperature of radiating surface b = constant. For black body b

= 5.67 X lOÂˇg W/m2

What are the role of baffles as beat lnten:b

K4.

genT

Answer- Baffles are circular discs of metal sheet having perforated sheet on one side to receive tubes. The baffles are placed outside the tube to increase the path and decrease the cross section of the path of the second fluid. The baffles

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also increase the velocity of the liquids outside the tubes and also make the liquid to flow more or less perpendicular to the tubes. This produces additional turbulence which decreases the resistance to transfer for heat transfer outside the tubes. 5.

Describe role or F'mned tube in beat transfer, Answer- The varieties of fins are available. Rectangular discs of metals may be placed at right angle to tubes. Spiral fins may be attached to tubes. Longitudinal fins are also used. Fins are used to decrease size of apparatus. They also increase rate of heat transfer. The air is present outside the tube while steam is present inside the tube. The heat transfer coefficient on steam side surface is high but on air side it is low. So the overall coefficient is shift to air side. The value of overall coefficient is low. The rate of heat transfer can only be increased by increasing surface area on air side. The surface area can be enhanced by attaching fins to outside the tubes.

LONG ANSWER OUESTIONS 1.

Describe the flow of heat through compound resistance in Series (Refer article 4.5)

Describe construction, working, advantage and disadvantage of Shell and tube heater (Refer article 4.10.1)

Describe construction, working, advantage and disadvantage of Multipass heater (Rerer article 4.10.2)

Describe construction, working, advantage and disadvantage of Two pass floating head heater (Rerer article 4.10.3)

Describe construction, working, advantage of liquid to liquid heat interchangers (Refer article 4.11.2)

MULTIPLE CHOICE OUESTIONS 1.

For black body the value or b Is equals to a. 5.67 X 10.8 W/m2 K4 b. 2.27 W/m2 K4 c. 1.22 X 10-8 W/m2 K4 d. 2 X 10-4W/m2 K4 Emissivity Is

a. ratio of energy emitted by actual body to energy emitted by black body. b. fraction of energy absorbed c. energy released d. ratio of energy absorbed to energy released at a given temperature 3. Grey body Is a body wbose Absorptivity radiation a. b. c. d.

Remain constant Increases Decreases First increase and then decrease

at all wavelength

Heat Transfer

The process of transfer of thermal energy from hot places to cold places by mixing of warmer portion with cooler portion of same material. a. b. c. d. The

Conduction Convection Radiation Evaporation Baftles are used to

a. b. c. d. The a. b. c. d. The

increase the path of the fluid increase the velocity of the liquids outside the tubes improve heat transfer All of the above overall coemcient of heat transfer is used in Conduction Convection Radiation Both a and b total amount of radiation emitted by black body is explained by

a. Stefan-Boltzmann Law b. First Law of thermodynamics c. Second Law of thermodynamics d. coulomb's law To StefanÂˇBoltzmann Law, energy radiated is directly proportional

a. b. c. d.

Absolute temperature Fourth power of absolute temperature Pressure Time

ANSWERS l.a

2.a

3.a

4.b

S.d

6.d

7.a

S.b