## 1. heat and thermal expansion

Introduction

In this chapter, we will study some of the thermal properties of matter.

This topic discusses various thermal phenomena and how a matter behaves when subjected to the flow of thermal energy. We are specifically concerned in

• Thermal expansion
• Heat and calorimetry
• Transfer of heat

We all have common-sense notions of heat and temperature. Temperature is a measure of ‘hotness’ of a body. A kettle with boiling water is hotter than a box containing ice. In physics, we need to define the notion of heat, temperature, etc., more carefully.

When the body is heated, various changes take place. It could expand, it can become hotter, it can change phase etc.  Temperature is a measure of the hotness of a body. When water boils or freezes, its temperature does not change during these processes even though a great amount of heat is flowing into or out of it.

You might have noticed that you feel hotter on a sunny afternoon as compared to a windy night. This is because of the difference in temperatures. Temperature is very high in the afternoon as compared to night. This chapter basically gives us the information about thermal properties of matter where we will study about the properties of different substances by virtue of heat/heat transfer.

Temperature and heat

Temperature is the relative measure or indication of the hotness and coldness of a body. A hot cooker is said to have higher temperatures and ice cubes to have lower temperature. An object at a higher temperature is said to be hotter than the one at a lower temperature. The S.I unit of Temperature is Kelvin (K).

A cup of hot soup and cold ice cream.

Heat

When we put a cold spoon into a cup of hot tea, the spoon warms up and the tea cools down as they were trying to equalize the temperature. Energy transfer that takes place solely because of temperature difference is called heat flow of heat transfer and the energy transferred is called heat.  The S.I. unit of heat transfer is expressed in Joule (J).

Measurement of Temperature

A physical property that changes with temperature is called thermometric property. When a thermometer is put in contact with a hot body, the mercury expands, increasing the length of the mercury column, which can be calibrated and later be used to measure temperature.

This was one such example, there are many such which enable us to measure temperature.

There are three scales of measurement of Temperature.

• Celsius scale
• Fahrenheit scale
• Kelvin scale

The standard scale of measurement of temperature is Kelvin scale.

1. Celsius scale:   It defines the ice point at 0 degree Celsius and the steam point temperature as 100 degree Celsius. The space between 0 and 100 degree Celsius is equally divided into 100 intervals.
2. Fahrenheit Scale: It defines the ice-point temperature as 32 F and the steam point is 212 F. The space between 32 F and 212 F is divided into 180 intervals.
3.  Kelvin scale:  Kelvin scale is a scale of measuring temperature, the melting point of ice is taken as 273 K and the boiling point of water at 373 K. The space between these is divided in 100 intervals. This is also known as the absolute scale of temperature as it has only positive values of Temperature. This scale has been adopted as the standard scale of measuring Temperature.

To convert a temperature from one scale to the other, we must take into account the fact that the zero temperatures of the two scales are not the same. Below is the relation between different scales of temperature.

Ideal gas equations and absolute Temperature

We have Liquid-in-glass thermometers like mercury thermometers, these thermometers do not give accurate readings for temperature other than the ice point and boiling point because of differing expansion properties of liquid.

A thermometer that uses a gas however gives the same readings regardless of which gas is used. This is considered to be a more accurate thermometer than liquid-in-glass thermometer.  Experiments show that all gases at low densities exhibit the same expansion behavior. The variables that describe the behavior of a gas of given quantity (mass) are

1. Pressure
2. Temperature
3. Volume

There are some laws that are followed by gases of low density. These laws are:-

1.  Charles’s law:  This law states that at constant pressure, volume and temperature of the gas are directly proportional for a fixed quantity of gases.

V α T  at constant P    or  V/T= constant

1.  Boyle’s law: This law states that at a constant temperature, the volume of the gas is inversely proportional to the pressure of gas for a fixed quantity of gases.

V α 1/P    at constant Temperature T  ;   PV= constant

1.  Avogadro law: At constant Pressure and Temperature, equal volume of gases contains equal number of molecules of gas. In other words, we can say that at constant P and T, the Volume of the gas is directly proportional to the number of molecules of gas.

At constant  P and T,    V α n

If we combine these three laws we will get   V α   n T/P; PV  α  nT

To remove the proportionality sign we add a constant R.  PV= nRT

Above equation is called the ideal gas equation and R= constant of proportionality is called the gas constant.   R= 8.31 J mol-1 K-1

Absolute zero temperature

This point, where all the atoms have been completely stopped relative to each other, is known as "absolute zero" and corresponds to the number zero on the Kelvin temperature scale. An object cannot be cooled below this point because there is no atomic thermal motion left to stop.

Can absolute zero ever be reached?

Physicists acknowledge they can never reach the coldest conceivable temperature, known as absolute zero.

The zero on a Kelvin scale is called the absolute zero.  Absolute Temperature is equal to minus 273-degree Celsius or 459.67 degrees Fahrenheit.

Thermal expansion

Thermal expansion is the tendency of matter to change in shape, volume, and area in response to a change in temperature. Temperature is a monotonic function of the average molecular kinetic energy of a substance.

Thermal expansion is caused by heating solids, liquids or gases, which makes the particles move faster or vibrate more (for solids). This means that the particles take up more space and so the substance expands

The amount by which it expands depends on three factors: its original length, the temperature change, and the thermal (heat) properties of the metal itself. Some substances simply expand more easily than others.

Thermal expansion is of three types:

• Linear expansion. The expansion in length is called linear expansion.

• Area expansion. The expansion in area is called area expansion.

• Volume expansion. The expansion in volume is called volume expansion.

If the coefficient of linear expansion is denoted by α

Coefficient of area expansion is denoted by β

Coefficient of volume expansion is denoted by γ

The relation between    α, β and γ is stated as   β= 2 α      and     γ= 3α

so , α : β: γ = 1 :2 :3

Anomalous behavior of water

Water shows some exceptional behavior that is when it is heated at 0°C, it contracts instead of expanding and it happens till it reaches 4 °C. The volume of a given amount of water is minimum at 4 °C therefore its density is maximum (Refer the Fig). After 4 °C water starts expanding. Below 4 °C, the volume increases, and therefore the density decreases. This means water has a maximum density at 4 °C.

Density of water is maximum and the volume of water is minimum at 4 degree Celsius. This is anomalous behavior of water. Because of this property of water in lakes and ponds freeze only at the top layer and at the bottom it does not, but if the water freezes at the bottom also then animal and plant life would not be possible.

The anomalous behavior of water, sometimes called the density anomaly, is due to strong intermolecular attractions between water molecules called hydrogen bonds. The large electronegativity difference between oxygen and hydrogen causes the hydrogen-oxygen bonds to be polar.

Specific heat capacity

Specific heat, the quantity of heat required to raise the temperature of one gram of a substance by one Celsius degree. The units of specific heat are usually calories or joules per gram per Celsius degree. For example, the specific heat of water is 1 calorie (or 4.186 joules) per gram per Celsius degree.

But let's try to understand the specific heat in detail.

Suppose you have 100 g of water in a vessel at 20 C temperature and you put that vessel on top of a stove (source of heat).  Place the thermometer inside it and hold a stopwatch. The heat from the stove will heat up the water and will raise its temperature that can be seen on the thermometer.

1. First note the time for increasing the temperature of the water from 20 degrees Celsius to 40 degrees Celsius (rise of 20 C).
2. Now you have water at 40 C, now again note the time for increasing the temperature of water upto 60 C (a rise of 40 C). You will notice that it takes double the time if we double the rise of temperature.

From the above experiment, we have the following conclusion.

Heat required to raise the temperature of a substance is proportional to the rise in temperature

Now we will do this experiment again but now with double quality. We now have 200 g of water at 20 C in a vessel which is kept on a stove and keeping all other things the same.

1. If we now try to raise the temperature of it upto 40 C and note the time of it.  We will notice that you need double the time as we got when we had only 100 g of water. (case 1)

Thus, Heat required to raise the temperature of the substance is proportional to the amount of substance.

Now in the next experiment, we change the liquid from water to oil. We take 100 g of oil at 20 C in a vessel keeping all other things the same.

1. If we now try to raise its temperature upto 40 C and note the time of it. You will get the time that is very less as compared to we get in case 1

Thus, the Heat required to raise the temperature of the substance depends on the nature of the substance.

The above series of experiments shows that the quantity of heat required to warm a given substance depends on its mass, m, the change in temperature, ΔT and the nature of the substance. The change in temperature of a substance, when a given quantity of heat is absorbed or rejected by it, is characterized by a quantity called the heat capacity of that substance.  Every substance has a fixed value of heat capacity.

Now you will understand the definition of specific heat more clearly.

Specific heat is defined as the amount of heat per unit mass absorbed or rejected by the substance to change its temperature by one.

Molar heat capacity

Heat capacity per mole of the substance is defined as the amount of heat (in moles) absorbed or rejected (instead of mass m in kg) by the substance to change its temperature by one unit.

Mathematically ,   q = n Cm ΔT   ;  Cm= q / (n ΔT)

Here q= heat absorbed in Joules (J), n= number of moles,

Cm = molar specific heat expressed in J mo-1K-1 or J mol-1C-1.

Heat transfer can be achieved by keeping either pressure or volume constant, accordingly, we define Cv and Cp. Let us discuss this now.

Molar-specific heat capacity at constant volume (Cv)

If the volume of the gas is maintained during the heat transfer, then the corresponding molar-specific heat capacity is called molar-specific heat capacity at constant volume (Cv).

Water has the highest specific heat of capacity because of which it is used as a coolant in automobile radiators and in hot water bags.

Molar-specific heat capacity at constant pressure (Cp)

If the gas is held under constant pressure during the heat transfer, then the corresponding molar-specific heat capacity is called molar-specific heat capacity at constant pressure (Cp).

A fun thing to do: Virtual lab

Below is the link of the states of matter simulations.

States of matter

What can we do in this simulation?

• We can choose from the options of gases available ( Neon, Argon, Oxygen and water)
• Then we can choose the state of matter from solid, liquid and gas.

We can then observe the temperature at which these gases are in different states. Like if we choose Water and Gas then the temperature would be around 373K or more, which says that water will be in gaseous form at 373 K and above.

• We can also choose one gas and then raises or lower its temperature and with the help of the motion of its atoms or molecules we can say whether it is in liquid , gaseous or solid states

## 2. calorimetry and heat transfer

Calorimetry

Calorimetry is made up of two words calorie which means heat and metry which means measurement.

When two bodies of different temperature are allowed to share heat, they attain a common temperature. If it is assumed that no heat is received from or given to anybody outside the system and if there is no chemical reaction involved in the process of sharing then,

Heat gain by the colder body= Heat loss by the hotter body

The above statement is called the principle of calorimetry and this is based on the law of conservation of energy.

A calorimeter consists of a metallic vessel and a stirrer both are made of the same material (copper or aluminium) and the vessel is kept in a wooden jacket so that there is no heat loss .A mercury thermometer can be inserted through a small opening in the outer jacket.

Change of state

Depending on temperature and pressure, all matter can exist in a solid, liquid and gaseous state. These states of matter are also called phases of matter.

The change of state from solid to liquid is called melting and from liquid to solid is called fusion. It is observed that the temperature remains constant until the entire amount of solid substance melts. That is both the solid and the liquid state of the substance co-exist in thermal equilibrium during the change in state from solid to liquid.

The temperature at which the solid and the liquid state of the substance is in thermal equilibrium with each other is called its melting point. The change of state from the liquid to vapour is called vaporisation.

It is observed that the temperature remains constant until the entire amount of liquid is converted into vapour.

The temperature at which the liquid and the vapour states of the substance coexist is called its boiling point. The change from solid to vapour state without passing through the liquid state is called sublimation and substance is said to sublimate.

As altitude increases, the density of the air becomes thinner, and thus exerts less pressure. At high altitudes, external pressure on water is therefore decreased and will hence take less energy to break the water. If less energy is required it means less heat and less temperature which means that water will boil at a lower temperature.

Latent heat

Latent heat is defined as the heat or energy that is released during a phase change of a substance. It could be either from a gas to a liquid or liquid to solid and vice versa. Latent heat is related to a heat property called enthalpy.

Latent heat   L= heat absorbed during transition/ mass = Q /m

However, an important point that we should consider regarding latent heat is that the temperature of the substance remains constant. As far as the mechanism is concerned, latent heat is the work that is needed to overcome the attractive forces that hold molecules and atoms together in a substance.

Let’s take an example. Suppose a solid substance is changing to a liquid, it needs to absorb energy to push the molecules into a wider, more fluid volume. Similarly, when a substance changes from a gas phase to a liquid, their density levels also need to go from lower to a higher level wherein the substance then needs to release or lose energy so that the molecules come closer together. In essence, this energy that is required by a substance to either freeze, melt or boil is said to be latent heat.

Two types of Latent heat

• Latent heat of fusion
• Latent heat of vaporisation

Latent heat of fusion:   It is the amount of the heat which is required to change the phase of the solid into liquid for unit mass at constant temperature.

For example: Latent heat of fusion of water is 33×105 J/kg. It mean to melt 1 kg of ice into water 33×105 J heat is required.

Latent heat of vaporisation: It is the amount of heat which is required to change the phase of the liquid into vapour for unit mass at constant temperature.

For example: Latent heat of water is 22.6 × 105 J/kg. It means to change 1 kg of water into vapours 22.6 × 105 J  heat is required.

Heat transfer

Any matter which is made up of atoms and molecules has the ability to transfer heat. The atoms are in different types of motion at any time. The motion of molecules and atoms is responsible for heat or thermal energy and every matter has this thermal energy. The more the motion of molecules, the more will be the heat energy. However, talking about heat transfer, it is nothing but the process of transfer of heat from a high-temperature body to a low temperature one.

There are three mechanisms of heat transfer whose name is given as conduction, convection and radiation.

• Conduction occurs within a body or between two bodies in contact
• Convection depends on the motion of mass from one region  to another,
• Radiation is heat transfer by electromagnetic radiations such as sunshine, with no need for matter to be present in the space between bodies.

Conduction

Conduction is the mechanism of transfer of heat between two adjacent parts of a body because of their temperature difference .Suppose one end of a metallic rod is put in a flame the other end of the rod will soon be so hot that I cannot hold it with your bare hands.

Here, heat transfer takes place by conduction from the hot end of the rod through its different parts to the other end. Gases are poor thermal conductors while liquids have conductivities intermediate between solids and gases.

The rate of heat energy flowing through the rod becomes constant at steady state. It is given by, Rate of flow of heat

Where K= thermal conductivity of material

A= cross-section area; d= distance between the two end

T2 and T1 are the temperatures of hotter and colder bodies. Following are the examples of conduction:

• Ironing of clothes is an example of conduction where the heat is conducted from the iron to the clothes.
• Heat is transferred from hands to ice cubes resulting in the melting of an ice cube when held in hands.
• Heat conduction through the sand at the beaches. This can be experienced during summers. Sand is a good conductor of heat.

Convection

Convection is a mode of heat transfer by actual motion of matter. It is possible only in fluids. Convection can be natural or forced.

In natural convection, gravity plays an important part. When a fluid is heated from below, the hot part expands and therefore becomes less dense. Because of buoyancy, it rises and the upper colder part replaces it. This again gets heated and rises up and is replaced by a relatively colder part of the fluid. The process goes on.

In forced convection material is forced to move by a pump or some other physical means. Examples of forced convection are the circulatory system, cooling system, and heat connector of an automobile.

Radiation is the transfer of heat by electromagnetic waves such as visible light, infrared and ultraviolet rays. Everyone has felt the warmth of the sun’s radiations and intense heat from a charcoal grill or the glowing coal in the fireplace. Most of the heat from these bodies reaches you not by conduction or convection in the intervening air but by radiation. This heat transfer would occur even if there were nothing but a vacuum between you and the source of heat.

All bodies emit radiant energy, whether they are solid, liquids or gases. The electromagnetic radiation emitted by a body by virtue of its temperature like the radiation by a red hot iron or light from a filament lamp is called thermal radiation.

When this thermal radiation falls on other bodies, it is partly reflected and partly absorbed. The amount of heat that a body can absorb by radiation depends on the color of the body.

Everybody both radiates and absorbs energy from their surroundings. The amount of energy absorbed is proportional to the color of the body.

A black body is an idealization in physics that pictures a body that absorbs all electromagnetic radiation incident on it irrespective of its frequency or angle.

Black-body radiation is the thermal electromagnetic radiation emitted by a black body within or surrounding a body in thermodynamic equilibrium with its environment (an idealized opaque, non-reflective body).

It has a specific spectrum of wavelengths that are inversely related to intensity and are only affected by the body's temperature, which is assumed to be uniform and constant for the sake of calculations and theory.

Emissive power: The amount of heat energy radiated per unit area of the surface of a body, per unit time and per unit wavelength range is constant which is called emissive power eλ of the given surface, given temperature and wavelength. Its S.I. unit is Js-1m-2.

Absorptive power: The ‘absorptive power ‘of a surface at a given temperature is the ratio of the heat energy absorbed by a surface to the total energy incident it at a certain time. It is represented by aλ. It has no units as it is a ratio.

Wein’s displacement law

The blackbody radiation curve for different temperature peaks at a wavelength is inversely proportional to the temperature.

Stefan- Boltzmann law

The Stefan- Boltzmann law  explains the relationship between total energy emitted and the absolute temperature

Stefan's Law states that the radiated power density of a black body is directly related to its absolute temperature T raised to the fourth power.

Greenhouse Effect

The greenhouse effect is the way in which heat is trapped close to Earth's surface by “greenhouse gases.” These heat-trapping gases can be thought of as a blanket wrapped around Earth, keeping the planet toastier than it would be without them.

The main gases responsible for the greenhouse effect include carbon dioxide, methane, nitrous oxide, and water vapor (which all occur naturally), and fluorinated gases (which are synthetic)

The largest source of greenhouse gas emissions from human activities in the United States is burning fossil fuels for electricity, heat, and transportation.

Newton’s law of cooling

Newton’s law of cooling describes the rate at which an exposed body changes temperature through radiation which is approximately proportional to the difference between the object’s temperature and its surroundings, provided the difference is small.

Definition: According to Newton’s law of cooling, the rate of loss of heat from a body is directly proportional to the difference in the temperature of the body and its surroundings.

Greater the difference in temperature between the system and surroundings, the more rapidly the heat is transferred and faster the body changes its temperature.

Newton’s law of cooling is given by,

Where,

• Tt = temperature of the body at time t and
• Ts = temperature of the surrounding,
• k = Positive constant that depends on the area and nature of the surface of the body under consideration

A fun thing to try: Virtual lab

Below is the link of the simulation of the Black Body radiation