Heat

8. HEAT

Heat

The energy that is being transferred between two bodies as a result of temperature difference is called heat. Once it is transferred from one body to another body it becomes the internal energy of the receiving body. Heat is defined as long as the energy transfer is taking place. Heat in a body or heat contained by the body is meaningless.

Heat is the internal energy of the body. A hot body has more internal energy than an identical cold body. When a hot body is kept in contact with a cold body, the cold body warms up and the hot body cools down i.e., the internal energy of the cold body increases and the internal energy of hot body decreases. Thus heat is a form of energy which causes the sensation of hotness.

Measurement of heat

The branch of science that deals with the measurement of heat is Calorimetry. Units used to measure heat are as follows:

1. C.G.S unit : Calorie(cal)

Calorie: it is defined as heat required to raise the temperature of 1g of water through 1 degree Celsius from 14.5⁰C to 15.5⁰C.

1. M.K.S unit: 1 Kilo Calorie (Kcal) = 1000 Calories.

2. S.I. unit: joule (J)

The units Calorie and joule are related as:

1 cal = 4.186 J (or nearly 4.2 J)

Temperature

Temperature is a quantity which tells the thermal state of a body (i.e., the degree of hotness or coldness of the body). It determines the direction of flow of heat when two bodies at different temperatures are placed in contact.

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At molecular level, when temperature increases (means body is gaining heat), we say kinetic energy of molecule increases.

Measurement of Temperature

The S.I. unit of temperature is Kelvin (K). The other most common unit of temperature is degree Celsius (^oC). The relation between Kelvin and degree Celsius is:

T (K) = (273 + t) ^oC

A degree on Celsius is part of the interval between the ice point and the steam point.

A degree on Fahrenheit scale is part of the interval between the ice point and the steam point. 1 centigrade degree = Fahrenheit degree

The relation between Fahrenheit scale and Celsius scale is

The zero of the absolute scale is the temperature at which the molecular motion ceases and the average kinetic energy of molecules becomes zero. Thus the zero of absolute is not the ice point.

Absolute zero is the lowest attainable temperature. No temperature can be less than this temperature. Therefore this scale has no negative temperature.

T K = (273 + t)^oC.

The branch of science that deals with measurement of temperature is known as Thermometry.

Difference between Heat and Temperature

CALORIMETRY

Heat is a physical quantity, hence we can measure it. The science of measurement of heat is Calorimetry.

Calorimeter: The instrument which is used for measurement of heat is called a calorimeter. It is usually a cylindrical vessel made of copper with a stirrer. Copper is used as it is a good conductor.

Amount of heat absorbed or given out by a body depends upon the following factors:

1. Mass of the body (m).

2. The rise or fall in temperature of the body (T)

3. The nature of the material which the body is made of

Now we can say that: Q ∝ mΔT

Or, Q = msΔT (1)

Where, s is a constant which explain heat absorption in terms of nature of material.It is a physical quantity which is known as specific heat or specific heat capacity.

From (1), s = $\frac{Q}{m\mathrm{\Delta}T}$

Specific Heat capacity: Specific heat capacity of a material is the amount of heat required to increase the temperature of unit mass of the material by 1⁰C. Specific heat depends upon the material; it is independent of the mass of the material.Specific heat of water is 1 cal/gm/⁰C in C.G.S. units. This means that to increase the temperature of 1 gm of water through 1⁰C, the heat required is 1 cal.

Specific heat of ice is .5 cal/gm/⁰C in C.G.S. units. This means that to increase the temperature of 1 gm of ice through 1⁰C, the heat required is .5 cal.

Among all the solid and liquid substance water has maximum capacity to store heat for a given rise of temperature. This is because water has maximum specific heat capacity. Similarly among all substance Lead experiences maximum rise of temperature for a given amount of heat as its specific heat capacity is least.

Illustration: Three bodies are supplied heat at the same rate. The masses of the bodies and the specific heat capacities are given below. Which of these will show the more rise in temperature?

(a) 2 kg, .25 units (b) 1.5 kg, .1 units

(c) 3 kg, .072 units

From the above equations we can say that T₂ >T₃ >T₁

So (b) will shows a higher rise in temperature compared to (a) and (c)

Thermal Capacity(C): Thermal capacity of a body is the quantity of heat absorbed to raise its temperature through 1⁰C.

Heat absorbed by a body = ms T

By definition, raise in temperature is 1⁰C

Heat absorbed by the body = ms (1) = ms

Thermal capacity C = ms

Thermal capacity of depends upon the mass of the body and the kind of material it is made of.

Water Equivalent (W): when same quantity of heat is supplied to a body and to water such that rise in temperatures is 1⁰C to each, then the mass of water is said to be water equivalent of the body.

By definition, Heat absorbed by the body = Heat absorbed by water

m_body s_body1⁰C = Ws_water1⁰C

As s_water is 1 cal/g⁰C

W= m_bodys_body

Types of Changes of State and the Temperatures at Which They Occur

Matter can exists in three states- solid, liquid and gases. One state can be converted into another. During the state change temperature of matter remains constant. Let us study the change of one state to another and the temperature at which they occur.

• Melting and Melting Point

The conversion of a solid to liquid form is melting. The temperature at which a substance which is being heated begins to melt under normal atmospheric pressure is called its melting point.

• Freezing and Freezing Point

The conversion of liquid to solid form is freezing. The temperature at which a liquid rejecting heat begins to solidify under normal atmospheric conditions is called its freezing point.

• Vaporization and Boiling Point

The conversion of a liquid to vapour is called vaporization. The temperature at which a liquid receiving heat begins to vaporize under normal atmospheric condition is called its boiling point.

• Condensation and Condensation Point

The conversion of a vapour to liquid is called condensation. The water at which a gas rejecting heat begins to liquify under normal atmospheric conditions is called as condensation point.

• Sublimation and Sublimation Point

The conversion of a solid into vapour is called sublimation. The temperature at which a solid vaporize under normal atmospheric conditions is called its sublimation point.

Whenever matter changes from one state to another state, heat is either absorbed or released by the substance. Heat absorbed or released by the body is called as latent heat.

Latent Heat (L)

It was experimentally found that the quantity of heat (Q) absorbed or released is directly proportional to the mass of the substance (m) which changes its state.

Q ∝ m

Q = mL

Latent heat of a substance is the quantity of heat required to change the state of a unit mass of a substance without any change in temperature.

L.H of a substance is the quantify of heat required to change the state of unit mass of the substance without.

A substance can have two types of phase change

1. Solid to liquid

2. Liquid to gas

For these types of phase change, we define two types of latent heats which are mentioned below in the table:

*** Steam at 100⁰C causes more burns that water at 0⁰C. Why?

Steam condenses when it comes in contact with the body. During condensation of every 1 gm of steam, 540 cal of latent heat of vaporization is given back. This extra heat delivered by steam causes severe burns than water at 100⁰C

*** Ice at 0⁰C is much cooler to touch than water at 0⁰C. Why?

When we touch water at 0⁰C we feel cool because the cool water absorbs heat from the body. But when we touch ice at 0⁰C it start absorbing extra 80 cal of heat for every gram of ice melting from our hand and hence we feel cooler.

Journey from ice at 0⁰C to steam at 100⁰C

Suppose mass of ice is m gram. During state change from ice to water at 0⁰C, ice absorbed heat (Q) = mL_F. After that temperature of water increases and water consumes heat (Q) = msT (where T=100⁰C). Now water at 100⁰C converts into steam at 100⁰C and absorbed heat (Q) = mL_V.

Illustration: What is the maximum amount of heat that can be supplied to 1 kg of ice at its melting point without changing its temperature?

Solution: When heat is supplied to 1 kg of ice without change of temperature, it means change of state is occurring.

Maximum amount of heat supplied to 1 kg of water at its melting point without change of temperature = the heat supplied to melt 1 kg of ice to 1 kg of water at 0⁰C.

The Principle of Calorimetry

When two bodies with different temperature are put in contact with each other, heat transfers between them. Heat flows from body which has higher temperature to other body which is at lower temperature. Temperature of the body which is absorbing heat increases, whereas temperature of body which is losing heat is decreases. This process continues until final temperature of both body become equal or we say both body reaches to thermal equilibrium condition.

During the attainment of thermal equilibrium, the heat which is lost by the hot body is equal to heat gained by the cold body.

Considering the law of conservation on energy, we can say that

Heat lost by hot body = Heat gained by cold body.

The above said principle is the principle of Calorimetry.

The principle of Calorimetry is used to calculate following things:

1. Equilibrium temperatures when hot and cold bodies are brought into contact with one another.

2. The latent heat of a body.

3. The specific heat of a body.

Consider a hot substance P of mass m₁, specific heat capacity s₁ at temperature ⁰C, mixed with a cold mixed with a cold substance Q of mass m₂, specific heat capacity s₂ at a temperature ⁰C , such that they attain a constant equilibrium temperature .

Heat lost by hot substance: m₁s₁(θ₁−θ)

Heat gained by colder substance: m₂s₂(θ−θ₂)

According to principle of Calorimetry:

Heat lost by hot substance = Heat gained by colder substance

m₁s₁(θ₁−θ) = m₂s₂(θ−θ₂)

Illustration: A solid of mass 25g (Sp. Heat capacity 0.8 J/g^oC) and at 120^oC is placed in 100 g of water at 20^oC. Calculate final temperature of mixture.

Solution:

Heat given out by solid = mc = 25 0.8 (120 – x) = 2400 – 20 x

Heat absorbed by cold water = mc = 100 4.2 (x – 20) = 420 x – 8400

Heat given out by solid = Heat absorbed by water

2400 – 20 x = 420 x – 8400

440 x = 10800

x= 24.54^oC.

Heat Transfer

Heat is energy ‘in transit’ which flows due to temperature difference from a body at higher temperature to a body at lower temperature. This transfer of heat from one body to another body can take place by three different routes:

(i) Conduction (ii) Convection (iii) Radiation

Conduction

Conduction is a process of transfer of heat from the hot end to the cold end from particle to particle of the medium without the actual migration of the particle of the medium.

Since medium is required for the transfer of heat by conduction, therefore, conduction is not possible in vacuum. In solids, heat is transferred mainly by the process of conduction.

Explanation of Conduction

Each solid is made up of atoms. In solids, heat energy is transferred from the hot end to the cold end by the vibrations of its atoms. The atoms at the heated end absorb energy and begin to vibrate with large amplitude without leaving their positions. They collide with the neighboring atoms and transfer a part of energy to them. These atoms on gaining heat energy now begin to vibrate with large amplitude and collide with the other neighboring atoms, transferring a part of energy to them. This process continues till the entire arrangement of atoms, called lattice, begins to vibrate. Thus heat is transferred from the hot end to the cold end. In this process the atoms of medium do not leave their positions, but they transfer energy through their vibrations. The rate of heat transfer by this process is not much.

Substances which allow heat to pass through them easily are called the good conductors of heat. For example, metals and mercury are good conductors of heat.

The substances which do not allow heat to pass through them easily are called the poor (or bad) conductors or insulators of heat. Non-metals such as glass, wood cloth, air, pure (distilled) water, wax, paper, clay, etc., are the bad conductors of heat.

Convection

Convection is a process of transfer of heat by the actual movement of the medium particles.

Liquids and gases are the bad conductors of heat. They are heated mainly by the process of convection. In a solid, the atoms cannot move, leaving their positions. So solids are not heated by convection. A medium is required for the transfer of heat by convection. Heat cannot be transferred by convection in vacuum.

By the process of convection, the transfer of heat is always vertically upwards. The reason is that the medium particles near the source of heat the absorb heat from the source and they start moving faster. As a result, the medium at this place becomes less dense so it rises up and the medium from above being denser moves down to take its place. Thus a current is set up in the medium from above being denser, moves down to take its place. Thus current is called convection current. The current continues till the entire liquid acquires the same temperature.

Radiation

Radiation is the process of heat transfer in which heat directly passes form one body to the other body without affecting the medium. The heat from sun reaches earth by this process.

In vacuum, heat is transferred only by the process of radiation. The heat energy transferred by the process of radiation is called the radiant heat or the thermal radiation. Thermal radiations are in form of electromagnetic waves. These waves can travel even in vacuum. They travel in all directions in straight line with a speed, equal to the speed of light (3 10⁸ m s^-1). They do not heat the medium through which they pass. They are reflected by a polished and white surface. They are refracted through a transparent medium like rock salt crystal etc. They are absorbed by the dull and black surface.

The absorption power is different for different bodies. A dull or black surface is better absorbers of radiant eat than a polished or white surface. A body coated with lamp black absorbs up to 95% of the radiant heat falling on it.

The emission power of different bodies at the same temperature is different. A dull or black surface emits more heat energy than a polished or white surface when both are at the same temperature.

Good absorbers are good emitters, while the poor absorbers are poor emitters.

Mechanical Equivalent of Heat

Mechanical equivalent of heat is the ratio of mechanical work to the heat produced. It is denoted by J. experimental value of J = 4.186 J/cal.

Evaporation v/s Vaporization

Both evaporation and vaporization involve a change of state from liquid to vapour, but both processes differ from each other in many ways. Following is the difference between them:

Thus, a liquid absorbs heat during evaporation. This heat is provided either by the liquid or by the surroundings. As the evaporating liquid absorbs heat from the liquid, the liquid itself cools down.