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4.3 Latent Heat

What does the word “latent  heat “ mean?

Latent heat means hidden heat. This heat energy changes the state of a substance (phase change). The heat cannot be ‘seen’ because there is no rise in temperature of the substance.

 

Phase Change

When a phase change has occurred , latent  heat is absorbed or  released.

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Latent heat and kinetic theory

 

In a solid,the molecules are linked to the neighbours by forces of attraction. As the solid is heated , the molecules vibrate more strongly. When the solid reaches its melting point, the vibrations have become so strong that the links begin to give way. Extra energy is needed to overcome these forces and separate the molecules. This is called the latent heat of fusion. No temperature rise occurs during this process, because the latent heat of fusion is used to overcome the intermolecular binding forces. The average translational kinetic energy does not change, so the temperature remains constant.

In a liquid, the molecules are free enough to slide  around and change neighbours, but  they are still almost as close to each other as in a solid. The links are weaker but still effective. As the liquid is heated further, the kinetic energy of the molecules increases more. At the boiling point, the molecules break free from each other and become a gas. Energy is needed to overcome the remaining links. This is  called the latent heat of vaporisation.

No temperature rise occurs during this process, because the latent heat of vaporisation is used to overcome the intermolecular binding forces. The average translational kinetic energy does not change, so the temperature remains constant.

 

The Heating and Cooling Curve (Naphthalene)

 

Heating curve

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Melting point = 80o C          Boiling point = 218o C

AB= Solid ,   BC = solid  +  liquid   CD = liquid

DE = liquid  + gas     EF = gas

At  AB,CD and EF : 

The heat supplied increases the kinetic energy of naphthalene.So the temperature rises because the temperature is a measure of the average kinetic energy of molecules in a substance

At  BC,DE :

At  t1  and   t2 phase change has occurred.

The latent heat is absorbed to provide the energy to overcome the binding forces between the molecules. The energy absorbed does not increase the kinetic energy of the molecules, so the temperature remains constant.

Cooling curve

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Freezing point = 80o C     

Condensation point = 218o C

AB= Gas   BC = Gas + Liquid   CD = Liquid

DE = Liquid +  Solid     EF =  Solid

At AB,CD and EF :

Heat is released to the surroundings and the kinetic energy of the molecules decreases, resulting in a fall in the temperature of the  naphthalene because the temperature is a measure of the average kinetic energy of molecules in a substance

 

At BC,DE :

At  t1  and   t2 phase change has occurred.

The latent heat is released to the surroundings as the molecules become more closely pack.. The energy released does not  decrease the kinetic energy of the molecules, so the temperature remains constant

 

Definition and the S.I unit of Specific Latent Heat  ,l

The specific latent heat of fusion , lf  :

Is the quantity heat of energy required to change 1 kg of a substance from the solid state to the liquid state , without a change in temperature.

The specific latent heat of Vaporisation , lv  :

Is the quantity heat of energy required to change 1 kg of a substance from the liquid state to the gaseous  state , without a change in temperature.

The S.I. unit of lf  and lv  is  J  kg-1

The relationship between  m,l  and Q

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Where,

Q  =  the heat energy transferred to the substance

m =   the  mass of the substance

l   =   the  specific latent heat  of the substance  

 

Example  1

 

What is the quantity of heat required to melt  2.0 kg ice at 0 o C.

(The specific latent heat of fusion of ice = 3.34 x 105 J kg-1)

Solution

 

 

Example 2

How much energy has to be removed from 4.0 kg of water at 20o C  to produce a block of ice at   0 o C. (The specific heat capacity of water = 4.2 x 103  J kg-1 o C-1 .  specific latent heat of fusion of ice = 3.34 x 105 J kg-1)

 

Solution

 

 

Example 3

 

Calculate the heat required to convert 4 kg of ice at   15o C into steam at 100o C.   

( Specific heat capacity of ice  = 2.1 x 103J kg-1oC1,

  Specific heat capacity of ice  = 4.2 x 103J kg-1oC1,

  Latent heat of fusion of ice = 3.34 x 105 J kg-1 and

  Latent heat of vaporisation of water =    2.26 x 106 J kg-1 )

 

Solution

 

 

 

 

To determine the latent heat of fusion of ice

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The electrical power of the heater is recorded = P

The mass of each the two empty beakers is determined using the weighing balance.

Mass of empty beaker A = m1  

Mass of empty beaker B =  m2

When water starts to drip from the filter funnels at a steady rate, the heater in  Set A is switched on.

The stopwatch is started  and the empty beakers  A and  B  are placed beneath the filter funnels.

After a period of t , the heater in Set A is switched off.

The masses of both beakers of water , A and B are determined using the weighing balance.

Mass of beaker A +  water = m3  

Mass of beaker B + water = m4

Calculate mass of ice melted by the electric immersion heater,  m  = (m3 – m1) –  (m4 – m2)

Calculate the heat supplied  by the heater = Pt

Calculate the heat absorbed by the ice during melting  = mlf

On the assumption that there is no heat loss to surroundings;,

 Pt = mlf

 lf = Pt

                m

Precautions

 

(1)     The immersion heater must be fully immersed in the ice cubes to avoid or reduce heat loss

 

Discussions

The value of the specific latent heat  of fusion of ice ,lf determined in the experiment is larger than the standard value of lf.

This is because the experimental value of the mass of ice melted ,m less than the expected m due to some heat loss to the surroundings.

The smaller the mass m, the greater the

 specific latent heat of fusion of ice,lf,

    lf­  =   Pt

             m¯

 

 

To determine the latent heat of vaporisation of water

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The electrical power of the heater is recorded = P

The electric heater is switched on the heat the water to its boiling point.

When the water starts to boil at a steady rate , the stopwatch is started and the reading on the balance is recorded = m1

After  a time ,t the reading on the electronic balance is recorded again = m2

Calculate the mass of water evaporated,  m = m1 – m2

Calculate the heat supplied  by the heater = Pt

Calculate the heat absorbed by the water  during vaporisation  = mlv

On the assumption that there is no heat loss to surroundings;,

 Pt = mlv

 lv = Pt

                m

Precautions

 

(1)     The immersion heater must be fully immersed in the water to avoid or reduce  direct heat loss to the surroundings.

 

Discussions

The value of the specific latent heat  of vaporization of water  ,lv determined in the experiment is larger than the standard value of lv.

This is because the experimental value of the mass of  water evaporated  ,m less than the expected m due to some heat loss to the surroundings.

The smaller the mass m, the greater the

 specific latent heat of fusion of ice,lv,

    lv­  =   Pt

              m¯

 

 

Example  4

A 800 W electric heater is used to boil water. What is the time required to reduce the mass of water by 4 kg after the water has reached its boiling point?

[ Specific latent heat of vaporization of water = 2.26 x 106 J kg -1 ]

 

Solution

 

 

 

 

Example  5

0.5 kg of a solid is heated by a 100 W heater. The graph shows how the temperature substance varies with time.

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Calculate the specific latent heat of fusion of the solid.

 

Solution

 

 

Applications of Specific Latent Heat in Everyday Life

(1)     When we are engaged in strenuous activities ,  sweating cools our bodies. The sweat evaporates and the bodies heat is removed as the latent heat of vaporisation.thus our bodies temperature is decreased.

 

(2)   Drinks can be cooled by adding in several cubes of ice. When the ice is melting , the latent heat of fusion is absorbed from the drinks. The temperature of the drinks is lowered.

 

(3)   Food can be cooked by using steam. Food such as cakes, eggs, fish, buns and others receive a large amount of energy when the latent heat of vaporization of steam released from condensing steam.

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