10nature of heat etc

7/28/2019 10nature of Heat Etc

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DIAGNOSTIC /REMEDIAL TEST

10 THE NATURE OF HEAT

This test is one of a series in Introductory Physics made available on the Website of the

School of Physics, Monash University, Australia

(www. physi cs. monash. edu. au/ communi t y).This test is NOT for the purposes of assessment. It is to assist you in locating

misconceptions and misunderstandings and generally to assist you in your study of

Physics. You should work by yourself and at your own pace following the directions

given. It is not necessary to attempt the test all at once. You may like to do it bit-by-bit,

waiting until you have covered a particular topic in class or in your reading of your text

book or you may like to "plunge in " before you begin your study of the topic.

Questions are on the left hand (even-numbered) pages. While reading or working on

these, keep the right hand (odd-numbered) answer page covered. DO NOT PEEK

AT THE ANSWERS ON THE RIGHT HAND PAGE !

The test was compiled by and largely authored by Emeritus Professor Bill Rachinger

who would appreciate any comments or suggestions for improvement. These could be

sent to him at bi l l . r achi nger@sci . monash. edu. au orEmeritus Professor Bill Rachinger, School of Physics

Monash University, P.O.Box 27, Vic 3800 Australia

Diagrams were produced by

Mr Steve McCausland, formerly of Department of Physics, Monash University


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COVER THE RIGHT HAND (ODD-NUMBERED) PAGES.

DO NOT PEEK

1.You have probably said things like:

"Close the window and keep the heat out"

"The sun warms us"

"Water is heated on the stove"

All of these imply that heat is something that can travel from one object or place to

another.

What do you understand by "heat"? Is it

A. a substance something like a gas, or

B. some sort of waves, or

C. some sort of energy , orD. something which rises up, or

E. some type of rays ?

If you are dissatisfied with these, write a sentence or two describing your understanding

of "heat.

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

GO STRAIGHT TO THE NEXT QUESTION. DON'T CHECK YOUR ANSWER YET.

WAIT UNTIL YOU ARE INSTRUCTED TO DO SO.

2.

We can estimate by touch whether one object is "hotter" than another. A better way of

measuring this "degree of hotness" is to use a.................................................... This measures

................................................ which is a preferable term to "degree of hotness".

CHECK YOUR ANSWERS TO THE LAST GROUP OF QUESTIONS.


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1. C is the best response.

The term "heat" is used in the scientific sense to describe "energy which is being transferred".

Energy is a rather difficult concept which you will learn to understand and appreciate as you

progress through your course in Physics. There are many forms of energy (examples are

mechanical, electrical etc.) which can be transferred from one place to another or converted into

one of the other forms of energy. Heat, strictly speaking is "energy in transition" i.e. energy in

the process of conversion from one form to another. In this sense it is rather like "work"another idea you will encounter later in your study of Physics. Because heat describes energy

which is being transferred from one object or place to another there is often a tendency to think

of it as a material substance like a gas or fluid. Do not think of it in this way.

If your answer includes a reference to "waves" or "rays" or "rising up" you were thinking about

the means by which heat energy is transferred. This will be dealt with a little later.

2. A thermometer measures temperature.

"Temperature" as you will learn soon is a very precise term and is often confused with "heat".

Much of this confusion arises because of statements like "heat up the water" which could mean

either "transfer (heat) energy to the water" or "raise the temperature of the water". From thistype of situation students often get the wrong idea that temperature is "amount of heat". Do not

fall into this trap.

--------------------------------------

In order to understand the ideas of "heat" and "temperature" better it is useful to begin thinking

about some new and very important ideas. The first of these is Mechanical Energy.

INTERLUDE-- MECHANICAL ENERGY

In your studies of Mechanics you will become very familiar with the term "mechanicalenergy". For the present it is useful to be familiar with some simple ideas:

Energy can be supplied to a body (a car or an atom) so as to make it travel faster. In this case

the Kinetic Energy is increased. Kinetic energy is energy associated with motion and is in fact

equal to mv2 where m is the mass and v the speed of the body.

Another result of supplying energy (doing work) is to change the position of the body in the

earth's gravitational field. In this case of supplying energy to lift a body the gravitational

Potential Energy of the body is increased. Here the potential energy is associated with the

gravitational force exerted on the body by the earth.

------------------------------------

It is also useful to think about the atomic nature of matter since this will allow us to explore, at

an atomic level, what is meant by the temperature of an object and what happens when we add

heat energy and raise its temperature.

The next group of questions will be directed towards developing an atomistic view of solids,

liquids and gases with special reference to heat phenomena. When studying the behaviour of

large scale objects or processes it is often useful to have a knowledge of what is happening at

the atomic level.


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Let's think first about a monatomic gas, the simplest state of matter.

We envisage this gas as a swarm of atoms flying about in random directions colliding

with one another and with the walls of the container. The atoms are far apart and except when

they collide they do not exert any forces on one another. They behave rather like microscopic

billiard balls.

Imagine energy (heat) being added to the gas in a container of fixed volume. A closed

jam jar would be close to this condition. The energy contained in the gas must increase.Remembering the comments about energy in the previous Interlude, what do you think happens

to the atoms as energy is added to the gas.

A. The atoms get further apart on average

B. The energy holding the atoms together increases

C. The kinetic energy of the atoms increases

D. The average speed of the atoms decreases.

CHECK YOUR ANSWER TO THIS QUESTION.

4

Now let's discuss what happens when heat is

added to a solid.

You may have learnt that most solids consist

of a fairly regular arrangement of atoms held

together by interatomic forces.

A simple but useful model is of balls connected together by "interatomic springs" representing

the bonds between atoms. The atoms are not stationary but oscillate about an "average"

position.

We have just seen that when heat energy is added to a gas this appears as energy associated

with the translational motion. Write down what you think happens to the atoms of a solid when

heat energy is added.

ANS.

............................................................................................................................................................

.......

............................................................................................................................................................

.......


Fig.1


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3.

C is correct. The kinetic energy, the "energy of motion" mv2 increases. The temperature of

the gas is in fact very closely related to the average kinetic energy of the atoms. (The

temperature of the gas measured in degrees Kelvin is proportional to the average kinetic energy

of the particles in an ideal gas).

D is untrue. Since kinetic energy ( mv2) increases the speed v increases.

B is not relevant. In our model of a gas we treat the atoms as "free" i.e. not exerting any forces

on each other - this is reasonable because for most of the time an atom is far away from other

atoms.

You may have been tempted to choose answer A since you have probably learnt that "things

expand when heated". In this case however, the gas was in a container of fixed volume and so

unable to expand. Thus the average separation of the atoms would remain unchanged.

It is interesting to note that on adding energy to a fixed volume of gas the increase in kinetic

energy is accompanied by an increase in pressure. The pressure exerted by the gas on the wallsof the container is the result of the "battering" by the atoms striking and rebounding from it.

With an increase in speed of the atoms the battering becomes more severe - the pressure rises.

This can be observed with a car tyre which is close enough to being a constant volume

container. On a hot day the pressure will increase. One form of thermometer is based on this

principle. By measuring the pressure of a gas in a constant volume container we can measure

temperature.

4.

On heating a solid the added energy appears as energy associated with the vibration of the

atoms and the oscillations become more violent. Two forms of energy are involved here:

i) the potential energy associated with the interatomic forces (work is done in stretching the

interatomic bonds)

ii) the kinetic energy mv2associated with the motion.

Note that in both the gas and the solid the added energy appears as mechanical energy of the

constituent atoms.


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5

An interesting feature associated with atomic oscillation occurs when the temperature of a solid

is increased to a stage where the oscillations become so large that atoms are able to leave their

"home base" and exchange positions with their neighbours or to shove their way through

between neighbours. When this situation occurs what has happened to the material?

ANS.........................................


6

This brings us to the question of what happens when a monatomic liquid is heated. Remember

that in a liquid the atoms are fairly close packed but free to exchange places and "shove their

way through the crowd." When heat energy is added to a liquid this energy is associated with

............................................. of the atoms.


7

Let's see if you can explain evaporation ( the presence of a vapour associated with a liquid -easily detected when we smell petrol). Here you should remember two things, the existence of

some fast moving atoms as explained in the answer to Question 6 and the comment in the

answer to Question 5 about the forces holding the atoms together in a liquid. Try to explain

how some atoms (or molecules) can escape from a liquid.

............................................................................................................................................................

............................................................................................................................................................


8Remember that a temperature increase corresponds to an increase in the average speed of atoms

in a liquid. Discuss the effect of increasing the temperature of the liquid on the process of

evaporation.

............................................................................................................................................................

............................................................................................................................................................


9

What happens if you continue to increase the temperature of the liquid. Does anything dramatic

happen? Can you explain this in terms of behaviour of atoms.

............................................................................................................................................................

............................................................................................................................................................



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5.

It has melted. When the melting temperature is reached the regular structure of the solid is

loosened up to the extent that the atoms no longer oscillate about a fixed position but

re-arrangements can occur and the material exhibits some very dramatic changes in properties.

Hitting an ice cube with a hammer produces very different results from hitting a pool of water!

In a liquid the atoms still "hang together ", they are not free to move unhindered as in a gas.

The forces between the close packed atoms hold the group together.

6.

The added energy is associated with the motion (or the kinetic energy) of the atoms. The atoms

in a hot liquid move faster on the average than those in a cold liquid. Notice the use of the

phrase "on the average". The atoms in a liquid do not all travel at the same speed; some are fast,

some slow. As the temperature of a liquid is increased the average speed of the atoms will

increase, that is, there will be a larger number of fast-moving atoms.

7.

Those atoms which are travelling very fast can overcome the attractive force of the atoms at the

surface of a liquid and escape through the surface to form a vapour. This process is known asevaporation

8.

At a higher temperature there are relatively more atoms which are travelling fast enough to

escape. More atoms escape. The liquid evaporates more readily at a higher temperature.

9.

If the temperature is continually increased a stage is reached where the atoms escape in such

large numbers that the liquid becomes violently disturbed. This is boiling. It occurs at a well

defined temperature. In usual circumstances, liquid does not exist above this temperature.

------------------------------------------

You should now be in a position to interpret, in terms of the behaviour of atoms or molecules

and their motions, many of the phenomena associated with the general subject of heat e.g.

processes by means of which heat is transferred, latent and specific heats etc. We will develop

some of these ideas in the following pages.


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10.

When heat is added to a sample of solid or liquid the temperature of the sample rises. (This does

not always occur - The exceptional cases will be discussed a little later.)

If the same amount of heat energy is added to various samples of different substances of

different size, shape etc the temperature increase will vary from sample to sample.

Which of the following would you expect to be of importance in determining the temperature

rise of a particular sample.

A. its massB. its shape

C. its state of subdivision (i.e. single lump or small pieces)

D. its hardness or softness

F. its physical state (e.g. liquid water or solid ice)

G. the actual material (e.g. lead or copper).


11.

(a) The table below shows the amount of heat energy (number of energy units) required to

raise the temperature of three samples of copper by various amounts. Complete theblank spaces in the table.

Table 1. Number of heat energy units for different temperature rises in different masses

of copper.

Temperature

rise T

Mass of copper

0.2 kg 0.6 kg 1.0 kg

4C

10C

25C

9.6 units

60 units

72 units

180 units

48 units

120 units

This suggests a simple algebraic relationship between the amount of heat (Q), the temperature

rise (T) and the mass of copper (m).

(b) Write down this relation

Q =

(c) Remembering what was said in the answer to Question 10 about heating copper and

gold write down an algebraic relation connecting H,m and T for gold.

Q =

(d) These relations show that to produce twice the temperature rise in a given mass of a

particular substance we must supply ........................ the amount of heat energy.

(e) Also, to produce the same temperature rise in one-half the mass of a particular material

we must supply ......................... the amount of heat energy.

(f) To produce a temperature rise of 1C in 1 kg of copper requires .....................the amountof energy which would be required to produce a temperature rise of 1C in 1 kg. of

gold.

CHECK YOUR ANSWERS TO THIS QUESTION.


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10.

A, F and G are the important factors.

In relation to A the amount of heat required to produce a given temperature rise in a sample of a

particular substance is proportional to the mass of the sample.

The actual material (factor G) is important. To raise the temperature of 1 kg. of Copper by 1 C

requires three times the amount of heat energy than is needed to cause the same temperature

change in 1 kg of gold.Whether the material is in solid or liquid form (factor F) is also important. For example to raise

the temperature of 1 kg. of liquid water by 1C requires about twice the amount of heat energy

to raise the temperature of 1 kg. of solid ice by 1C.

11.

(a) The missing numbers are shown underlined

Temperature

rise T

Mass of copper

0.2 kg 0.6 kg 1.0 kg

4C

10C

25C

9.6 units

24 units

60 units

28.8 units

72 units

180 units

48 units

120 units

300 units

(b) The algebraic relationship linking all the numbers in the table is

Q = 12 mT for copper where T = temperature rise

(c) Q = 4 mT for gold

(d) twice

(e) one-half

(f) three times

These answers all illustrate the simple relationship

Q = c m T

which states that the heat energy input is proportional to the mass of the substance and the

temperature rise, the constant of proportionality being dependent on the particular

substance. This constant c is a physical property of the material called the specific heat

which is the heat energy input required to raise the temperature of 1 kg of the substance by

1celsius (or kelvin). It is usually defined for the situation where Q is expressed in

joule(J), m is kilograms(kg) and T in degrees celsius(C) or kelvin (K) in which the unitsof c are expressed as J C-1 kg-1 or J K-1 kg-1.


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12.

Now let us think about what happens to the heat energy which is added to a solid material and

brings about a rise in temperature. Remember our "model" of a solid as a regular arrangement

of atoms.

Where do you think this extra added energy goes to?

A. There is an increase in the amount of energy "locked up" in the individual atoms

B. The energy goes into the expansion of the solid (usually solids expand when heated)

C. The extra energy is associated with the vibration of the atomsD. The energy is distributed over the surface of the solid making it feel hotter when we touch

it.

ANS...................


13.

Let us now look at the situation of a saucepan of water being heated on your kitchen stove. At

first the temperature of the water will........ . Then a stage is reached when something ratherviolent happens. The water....... . As more heat is added this process continues.

During the time that this process continues, the temperature

A. continues to rise

B. stays the same

C. decreases.

ANS.................


14.

Consider some vegetables cooking in a saucepan of boiling water. Is it possible to cook themmore rapidly by "turning up" the gas or electricity thus increasing the rate at which energy is

supplied to the saucepan? Give the reason for your answer.


15.

We have seen that when heat energy is added to water at 100C the water boils but the

temperature does not rise. Where does this energy go:

A. It causes the molecules of water (H2O) to break up into constituent atoms of hydrogen and

oxygen

B. It makes the water molecules vibrate more vigorously about their fixed locations

C. It gives some water molecules sufficient energy to escape from the liquid

D. It causes the liquid to expand.

ANS..........



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12.

C is the answer. The heat (energy) transferred to the material appears as mechanical energy of

the constituent "particles" (atoms or molecules). In the case of a gas this is the kinetic energy

( mv2) of the freely moving atom or molecules.

In a solid where the atoms are not free but are tied down to particular locations they oscillate

about fixed positions. When heat (energy) is added to the solid they oscillate more vigorously

and there is a larger amount of energy (potential and kinetic) associated with this bigger

oscillation.In order to increase the amount of energy "locked up" in the individual atoms (Answer A)

exceptionally large amounts of energy would need to be added. The material would no longer

be a solid but a vapour.

Although the expansion of a solid (Answer B) is associated with the (lopsided) oscillation of the

atoms it is the total mechanical energy of the constituent atoms which accounts for the added

heat energy.

D is incorrect. The added energy is distributed uniformly throughout the material.

Similarly in liquids where the atoms have more freedom of movement than in a solid (they arenot tied to fixed locations) added heat (energy) is associated with the energy of motion of the

atoms.

13.

rise or increase

boils

B is correct. The temperature stays constant. You can verify this with a thermometer which is

calibrated to read up to more than 100C. This is typical of the boiling of all pure substances.

Some consequences of it are discussed in the next questions.

14.

The cooking will not be more rapid. We saw in the previous question that the temperature

remains constant (at 100C). Cooking can in fact be "speeded up" using a pressure cooker. Here

the water boils in a closed vessel at a high pressure. In this circumstance the water boils at a

higher temperature and the vegetables cook more rapidly.

15.

C is correct. Some molecules achieve a high enough kinetic energy to break loose from the

forces holding them in the liquid. At the boiling point all added energy is going into this

process. The molecules escape in large numbers and we observe this as boiling. The more

rapidly we add heat energy the more vigorous the boiling.

Water will dissociate appreciably into its constituent atoms as suggested in A only at very high

temperatures - in excess of 2000C. At 100C the effect is negligible.

B is incorrect. In a liquid the molecules are not tied to fixed locations. This is typical of a solid.

D. Although liquids expand (usually) with increasing temperature boiling water is at a constant

temperature at which no further expansion takes place.


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16.

We would expect that the amount of heat required to "boil away" a given mass of liquid would

depend very simply on the mass of the liquid.

If 10 heat units were required to boil away 2 kg. of water we would expect that ...........heat units

would be required to boil away 1 kg. of water.

Thus the amount of heat Q required to boil away m kg. of water would be given by

Q = ............If on the other hand we were boiling away ammonia (at -33C) we would require 3 heat units

for each kg. of ammonia.

Thus for ammonia the relation between H and m is

Q = ............


17.

We saw earlier that when a liquid boils the temperature does not change. A similar situation

occurs when a pure substance melts. For instance when heat is added to ice at 0C the

temperature of the ice does not rise but the ice melts.Which is the best "microscopic explanation" of this happening

A. Some water molecules vibrate more vigorously and break free from their fixed locations

B. The ice expands so much that it becomes a liquid

C. The ice molecules break up in to hydrogen and oxygen atoms which later join up to form

water molecules

D. The water molecules break free and form a vapour.

GO STRAIGHT TO THE NEXT QUESTION. DON'T CHECK YOUR ANSWER YET.

WAIT UNTIL YOU ARE INSTRUCTED TO DO SO.

18.

The amount of heat (Q) required to melt a piece of ice depends only on the mass (m) of ice. It isin fact given by

Q = 33.5 x 104 m

where Q is in Joule and m in kg.

The quantity 33.5 x 104 is the latent heat of melting of ice and is measured in Joule per kilogram

(J kg-1).

For other pure substances which always melt at a constant temperature the relation is of the

same form.

Q = L m

where Q is the amount of heat energy required to melt a mass m of the substance with

latent heat of melting L.

(a) Calculate the amount of heat energy required to melt 5 kg. of lead at its melting point

(327C) if its latent heat is 2.6 x 104 J kg.-1

(b) How much ice at 0C would be melted by the same quantity of heat.



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16.

5 heat units would be required

Q = 5 m for water

Q = 3 m for ammonia

In general the amount of heat (Q) required to vaporise (boil) m kg. of a substance is given by:Q = L m

where L is a constant, known as the latent heat of vaporisation which depends on the

particular substance.

If m is measured in kg. and Q in Joule then L is expressed in Joule kg-1 (Joule per kg.)

17.

A is correct. The added energy goes into the energy of motion of the individual molecules.

Some break away from their neighbours and from the surface of the ice joining other molecules

which are "free" to wander around in the liquid which surrounds the solid ice. Note that thesemolecules are not as "free" as those in a gas. In a liquid the molecules are held close to their

neighbours by strong forces which "hold the liquid together". In a gas the molecules are far

apart and are little influenced by one another.

B is not true. The ice is at a constant temperature.

C is not true. We saw earlier that the water molecules will break up only at very high

temperature.

D is inappropriate. Some substances sublime i.e. pass directly from a solid to a vapour state.

Ice does not do this, it melts i.e. passes from a solid to a liquid state.

18.

(a) The heat energy required is

Q = 2.6 x 104 x 5

= 13 x 104 joule

(b) The mass of ice which would be melted by this would be

0.39kg=1033.5x

1013x

=Q/L=m 4

4


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1419.

On a hot day you pour yourself a glass of cool (10C) water and put an ice cube (at 0C) in it.

The temperature of the water changes as shown in the graph.

(a) Which is the best explanation of the portion ab of the curve?

A. Energy is being extracted by the surrounding air

B. Energy from the water is being supplied to melt the ice

C. Some of the water is freezing thus making it colder

D. The water molecules are speeding up.

ANS............. Why are the other answers wrong?

(b) Which is the best explanation of the portion bc of the curve?

A. Nothing is happening. The water has now reached 0C and no ice is melting

B. All the ice had melted at point b and the water is now at a steady temperature of

0C

C. The ice is continuing to melt and melting is complete at point c

D. Some of the water is re-freezing.

ANS............. Why are the other answers wrong?

(c) Which is the best explanation of portion cd of the curve?

A. The ice which was present at point c is now beginning to melt

B. Heat is coming in from the surroundings to warm up the water

C. The latent heat of melting of ice is now being supplied to the water to warm it up

D. The energy of oscillation of the water molecules in the ice is increasing.

ANS.............. Why are the other answers wrong?



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19.

(a) B is the appropriate explanation. After putting the ice cube in the water the ice begins to

melt. The latent heat required for this is extracted from the water and the water cools as

indicated by section ab.

A is certainly incorrect. Since the water (10C or less) is cooler than the surrounding air some

heat would be flowing in from the surroundings i.e. heat would be extracted from the

surrounding air.

C is untrue. The water (being at a temperature greater than 0C) would not be freezing.

D would occur if the temperature were rising, not falling as it is in this case.

(b) C is the appropriate explanation. At b the ice and water are both at 0C. Heat flows into the

system from the surroundings but it does not increase the temperature. It is used in melting the

ice (supplying the latent heat of melting). The temperature remains constant until the ice is all

melted at point c.

A is incorrect. Ice is certainly melting because of the heat flowing in from the surroundings.

B and D are incorrect for the same reason.

(c) B is the appropriate explanation. Once the ice has completely melted at c the only

happening is that heat flows (soon we will discuss how heat flows from one body to another orfrom one place to another) in from the surroundings and the temperature of the system slowly

increases. There is no ice present so that A and C are incorrect. These suggest that heat would

be supplied to the water from the melting ice whereas the reverse is true. D refers to energy of

oscillation of the water molecules and this is appropriate only to the solid form of water i.e. ice.


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20

The graph above shows how temperature changes with time when heat is added at a constant

rate to 1 gram of water initially in the form of ice. The temperature rises for the first 105

seconds, stays constant until t = 440s and then rises again until t = 860s.

(a) What is the temperature represented by point A?.......

(b) What is the temperature represented by point B?.......

(c) Fill in the remaining points on the temperature axis of the graph.

In this particular experiment heat is added at the rate of 1.0 J per second.

(d) How much heat is added to the ice in the first 105 seconds?.........

(e) By how much does its temperature increase during this time?.............

(f) From this data calculate the specific heat of ice in J-1 kg-1C-1.?

(g) How much heat is required to melt the 1 gm. of ice?

(h) What is the latent heat of melting of ice?

(i) Calculate the specific heat of water.

(j) The water is heated at the same rate after reaching 100C. If the latent heat of vaporisation

of water is 2.26 x 106 J kg-1 for how long should the water be heated to boil away one half

of it?



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1821.

In order to freeze 1.0 kg. of water which was initially at 10C a certain amount of heat Q must

be extracted. Calculate how much heat is extracted using the values of specific and latent heat

given in the answers to the previous question.

Q = ......................................... .


22. For this question use values of specific and latent heat given in the answers to Question.2O.5 gm of steam at 100C is bubbled into 100 gm of water initially at 20C.

No steam escapes.

(a) What is the mass of the final amount of liquid

ANS...............

(b) What is the final temperature T of the liquid

(Hint: here you should do some "energy bookkeeping".

Consider how much energy is involved in

(i) condensing steam to water at 100C

(ii) cooling this water to the final temperature TC

(iii) heating the original 100 gm. of water from 20C to the final temperature TC.)

T =.............................



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1921.

Cooling processes are the reverse of heating processes. To reduce the temperature of a material

heat energy must be extracted from it. A liquid will solidify or a gas will condense if heat is

extracted from it. The quantities of heat energy involved are the same as in the heating

processes. For example the latent heat of melting is the same as the latent heat of solidification.

Freezing 1.0 kg. of water initially at 10C involves two processes:

(a) Cooling the water from 10C to 0C which involves the extraction of a quantity of heat

mcT = 1.0 x 4200 x 10 = 4.2 x 104J

where c = specific heat of water =4200 J kg-1C-1

and T =temperature drop = 10C

(b) Freezing the water which requires extraction of an amount of heat equal to

mL = 1.0 33.5 104 = 33.5 104 J

where L = latent heat of melting (or solidification)

= 33.5 x 104 J

The total amount of heat extracted is just the sum of these

i.e. Q = 37.7 x 104 J

22.

(a) Since no steam escapes and mass is conserved the final mass will be 105 gm.

(b) The steam in condensing will give up its latent heat to the system and will form 5 gm of

water at 100C. To reach the final condition (105 gm. of water at TC) this 5 gm of water

will be cooled to the final temperature TC and the initial 100 gm of water will be heated

from 20C to TC.

Thus the problem can be viewed as follows:

The heat required to heat 100 gm of water from 20C to TC

= Heat supplied by the condensation of 5 gm of steam

+ Heat supplied by 5 gm of water cooling from 100C to TC.In terms of the usual symbols:

m1 c(T - 20) = m2L + m2 c(100 - T)

where m1 = mass of initial water = 0.1 kg.

m2 = mass of steam = 0.005 kg.

c = specific heat of water = 4200 J kg-1C-1

L = latent heat of vaporisation (or condensation)

= 2.26 x 106J kg-1

This gives

T (m1 + m2) c = m2L + (100 m2 + 20 m1) c

C449.=4200.105

2.0)4200+(0.5+102.26.005=T 0

6


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23.

The graph shows how temperature changes

with time when heat is supplied at a constant

rate of 4 x 104 J per minute to a substance

initially solid at 0C

(a)What is occurring at t=2 min.

.............................................................

.............................................................

b)What is occurring at t=6 min.

.............................................................

.............................................................

.

(c)Draw in the space below the graph of temperature versus time if the same total amount of

heat is supplied to the substance at twice the rate (i.e. 8 x 10 4 J per minute) again starting at

0C.



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23.

(a) The substance begins to melt.

(b) Melting is complete. The substance is all liquid.

(c)

Since heat is being supplied at twice the rate the total energy required to heat the solid to

its melting point of 40C will be supplied in 1 minute (previously 2 min.). The energy

required to melt it completely will be supplied in a further 2 min. (previously 4 min.).

Finally the energy required for heating the liquid to 80C will be supplied in 2 min.

(previously 4 min.). The whole process has taken one half the time (5 min. as against 10min. in the first experiment).

Since the same total amount of energy is supplied the final temperature of 80C is the

same as in the earlier experiment.


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24.

We saw in an earlier question that the latent heat of melting of ice is many times greater than

that of lead. With which one of the following is this fact most closely associated

A. The energy required to break up the regular atomic arrangement in 1 gm of solid lead is

much less than that required to break up the arrangement of H2O molecules in 1 gm of ice

B. The energy of oscillation of the atoms in 1 gm of solid lead is much greater than that of the

H2O molecules in 1 gm of iceC. The energy of oscillation of the atoms in 1 gm of solid lead is much less than that of the

H2O molecules in 1 gm of ice

D. The energy possessed by the mobile atoms in 1 gm of liquid lead is less than the energy

possessed by the H2O molecules in 1 gm of water.

ANS..........


25.The following statements A - E refer to the behaviour of atoms in solids, liquids and gases.

A. Atoms slide past one another

B. Atoms in a regular array oscillate within small fixed regions

C. Atoms leave their fixed regions to wander

D. Atoms move freely at large (average) distances from one another

E. Atoms break loose from their neighbours and disperse to large distances from one another.

Which of A - E is associated with the energy involved in

(a) The specific heat of a solid..........

(b) The specific heat of a gas............

(c) The specific heat of a liquid.........

(d) The latent heat of melting............(e) The latent heat of vaporisation.......


26.

You are required to calculate the amount of heat required to completely vaporise a quantity of

water originally in liquid form at 0C.

Tick the quantities which you would need to know

[] The density of liquid water

[] The mass of liquid water

[] The specific heat of ice

[] The specific heat of liquid water

[] The density of steam at 100C

[] The latent heat of melting of ice

[] The specific heat of steam at 100C

[] The latent heat of vaporisation of water.



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24.

A is the appropriate response. The latent heat of melting is a measure of the amount of energy

required to bring about the collapse of the regular atomic array typical of a solid into the mobile

arrangement of atoms in the liquid. It is not directly associated with the energies of motion of

atoms in the solid (B and C) or liquid (D).

25.

The answers are

(a) B

(b) D

(c) A(d) C

(e) E

If you have answered some of these questions incorrectly you should re-read the answers

to questions 3-9.

26.

The quantities required are:the mass of liquid water m

the specific heat of water c

the latent heat of vaporisation of water L.

These allow the calculation of the quantity of heat Q using the relation

Q = (heat energy required to raise the temperature of the water from 0C to 100C)

+ (heat energy required to vaporise the water)

= mc 100 + mL


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27.

A material has the following properties:

specific heat of solid = cS

specific heat of liquid = cL

latent heat of melting = L

0.5 kg of the material is heated from 20C where it is solid to 140C where it is liquid. The totalamount of heat energy supplied is Q.

Calculate below an expression for the melting point T of the material.

(Hint: Remember the technique of "energy bookkeeping" used in Question 22.

Consider the amount of energy required to

(a) raise the temperature of the material to its melting point

(b) melt the material

(c) raise the temperature of the liquid to 140C.

T =



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2527.

As suggested in the hint, the total heat energy supplied will be the sum of three parts:

a) the energy required to heat 0.5 kg of the solid material from 20C to its melting point TC

i.e. 0.5 c S (T-20)

b) the energy required to melt 0.5 kg.

i.e. 0.5 L

c) the energy required to heat 0.5 kg of the liquid from TC to 140C

i.e. 0.5 c L(140-T)

The total heat energy supplied Q is the sum of these

Q=0.5[c S(T-20) + L +c L(140-T)]

2Q=c ST -20c S + L + 140c L c LT

T(c L-c S)= L - 20c S + 140c L-2Q

c-c

2Q-c140+c20-L=T

SL

LS


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COMMENTS

10nature of heat etc

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