#### Heat-temperature and molecular theory, Physics tutorial

Concept of Heat and Temperature:

Whenever we touch a kettle of boiling water, we will feel a burning sense. We will state that the water is hot. As well, when we hold ice block, our hand feels frosty and we sum up that the water is cold. We explain an object that has been given heat energy as hot. If we place a kettle of cold water on a heating stove, after some minutes, the water feels hotter as it has been given heat energy. Likewise, we depict as cold a body from which heat energy has been eradicated. For illustration, keeping a bottle of water in a refrigerator, you should have experienced that heat for all time flows from a hot object to a cold object.

Heat energy is the energy which is transferred from a hot object to a cooler object as an outcome of their difference in temperature.

Temperature is the degree of coldness or hotness of an object. Temperature is a property of an object that decides which way heat will flow if it is placed in contact with the other object. Generally heat flows from a body of higher temperature to one at lower temperature.

The device for measuring the temperature is thermometer.

Effects of Heat:

There are many heat effects which we experienced in daily basics are summarized as:

The addition of heat to the body will cause:

1) Change in temperature of the body apart from throughout a change of state.

2) Change of state of the body solid to liquid, liquid to gasses state.

3) Body expansion.

4) Modification in the physical property of a body like the electrical resistance, magnetic properties conductivity, density, elasticity and color of the body.

5) Thermionic emission, that is, the emission of electrons from the surface of metal.

6) Change in chemical properties of the body.

7) Changes in the volume and pressure of gases.

Kinetic Molecular Theory:

The molecular theory of matter supposes that the matter is made up of atoms which aggregate in molecules.

The molecule is a group of atoms of the similar or different elements joined altogether in a simple proportion. Such molecules are under the influence of two kinds of forces:

1) Attractive forces that prevent the molecule from moving apart.

2) Repulsive forces that prevent the molecule from moving closer.

There is generally a balance between such forces in a substance.

In solid substances, the attractive forces among molecules are so strong that the molecules don't move about freely. The molecules just vibrate around their mean positions sustaining a fixed volume and shape.

In liquids, the molecules are loosely held altogether through weak attractive forces. The molecules are free to move around within the liquid and are for all time in a state of random motion. Molecules of liquids and solids are held altogether by intermolecular forces.

In gases, the force of attraction among the molecules is much weak. The molecules are thus in constant motion having overcome the intermolecular force. They move much freely at a very high speed. They are for all time in the state of random motion and take up the shape and volume of their vessel or container.

The kinetic molecular theory supposes that:

a) Each and every substance is build up of tiny particles termed as molecules.

b) The molecules are in a constant state of arbitrary motion, colliding elastically by one other and changing their direction as an outcome.

c) There is for all time an attractive force among the molecules.

d) The volume of gas molecule is negligible as compared by the volumes of gas container.

Kinetic Theory description of Temperature:

It is stated that the molecules of a substance are in constant motion; thus, they have kinetic energy. The temperature of body is a measure of the average kinetic energy of its molecules.

Whenever you add heat to a substance, the motion of the molecules raises resultant in an increase in the average kinetic energy of the molecules of the substance, therefore, a raise in its temperature. On the other hand, whenever you remove heat from a body, the motion of its molecule reduces resultant in reduction in their average kinetic energy and a reduction in temperature.

It follows thus, that the temperature of a body is associated to the average kinetic energy of its molecules.

Kinetic Theory description of Expansion:

Whenever we heat a substance, its size increases, then we can state that it expands. Whenever the substance cools, it contracts that is, decreases in size.

According to the kinetic molecular theory, if an object is heated the molecules get more kinetic energy that enables them to overcome their intermolecular forces resultant in rise in vibration of the molecules and their displacement around their mean positions. The average distance among the molecules of the substance becomes bigger leading to a raise in the size of the substance. The increase based on the strength of the intermolecular forces. When such forces are strong, the expansion will be small and vice-versa.

The intermolecular forces are stronger in solids than in liquids and weakest in gases. Thus, if heat is applied, gases expand more than liquids and liquids expand more than solids.

Kinetic Molecular Theory Explanation of Change of State:

You are aware that substances exist in any of the three states of matter: solid, liquid and gas. By the help of heat energy, it is possible to transform a substance from one state to other. The change of state refers to the procedure of transforming a substance from one state of matter to other.

If a solid is heated its temperature rises until it reaches certain maximum temperature at which the molecules get maximum kinetic energy. At this maximum temperature, further heating does not raise the kinetic energy of the molecules however the heat energy (latent heat) is employed to break down the intermolecular forces binding the molecules of the solids in a regular prototype. The molecules then melt and move about freely as they are in the liquid state. The maximum temperature is the melting point of the solid. As well, the change from liquid to gas occurs in an identical fashion. The liquid temperature rises as it is heated and reaches its maximum temperature at which the molecule gets maximum kinetic energy.

Further heating (or latent heat) supplies the required energy to overcome the forces of attraction between the liquid molecules and changes the liquid to vapor devoid of temperature change. The molecules are then practically independent of one other and exist as a gas.

The energy required in this case is much greater than from solid to liquid and the latent heat is much greater. Elimination of heat energy from a substance outcome in the reverse procedure.

The heat needed to break down the intermolecular forces of attraction in a solid is the latent heat of fusion. The latent heat of vaporization is the heat required to overcome the forces of attraction among the molecules of the liquid.

Expansivity:

This is the fractional change in length or area or volume per unit change in the temperature at a specific constant pressure.

1) Linear Expansivity (α):

We can find out the extent that a unit metal substance modifies in length if its temperature changes by one degree. This quantity is termed as linear expansivity of the metal substance. This is symbolized by the symbol α (pronounced alpha).

The linear expansivity (α) of a substance is stated as the rise in length per unit length per degree rise in temperature.

In symbols, this is equivalent to:

α = (l2-l1)/[l121)] = e/l1θ

Here:

α = linear expansivity, l1 = length of metal at temperature θ1, l2 = length of metal at temperature θ2, θ = temperature rise given by (θ2 - θ1), e = expansion or increase in length (l2- l1)

α = Increase in length/(original length x temperature rise)

2) Area Expansivity (β):

Whenever we heat a solid, it expands in all directions that are the length, breath and height. This outcome in an increase in area and also in volume of the solid. This increase in area if the body is heated is termed as area or superficial expansion. This is represented by the symbol 'β' (pronounced beta).

Definition: The area or superficial expansivity, 'β', of a solid is the increase in area per unit area per degree Kelvin rise in temperature or the fractional rise in area per Kelvin rise in temperature.

Area expansivity β = change in area/(original area x temperature rise)

β = (A2 - A1)/[A1 x (θ21)] = a/A1θ

Here, a = increase in area (A2 -A1), A2 = area at temperature θ2, A1 = area at temperature θ1 and

θ = (θ2 - θ1)

Volume or Cubic Expansivity (γ):

An increase in volume if a body is heated is termed as cubic or volume expansion. We signify cubic expansivity having the symbol γ pronounced gamma.

Definition: The volume or cubic expansivity γ, is the increase in volume of a substance per unit volume per Kelvin increase in temperature or the fractional rise in volume per Kelvin rise in temperature.

Cubic expansivity (γ) = change in volume/(Original volume x temperature rise)

γ = (V2 - V1)/[V12 - θ1) ] =  v/V1θ

Here, v = increase in volume (V2 - V1), V2 = volume at temperature θ2, V1 = volume at temperature θ1 and θ = (θ2 - θ1)

The Relationship between Linear Expansivity (α), Area Expansivity (β) and Cubic Expansivity (γ)

If α is the coefficient of linear expansivity of a metal, its area expansivity (β) and volume expansivity (γ) are associated (α) by:

β = 2α

γ = 3α

We can as well write the given:

l2 = l1 (1 + αθ)

A2 = A1(1 + βθ) = (A1 + 2αθ)

V2 = V1 (1 + γθ) = (V1 + 3αθ)

Applications of Expansion:

1) Gaps are left between rails in railway lines to consent for free expansion and contraction of the rails. Devoid of the gaps, the rail joints will swell up on hot days, the railway line will clasp and trains would be derailed.

2) The end of steel structure of long bridges rests on rollers that permit for the expansion and contraction of the bridge devoid of weakening the structure.

3) Telegraph wires are permissible to sag if fixed in the warm, raining season, so that they don't snap if they contract in the cold harmattan.

4) A bimetallic strip is employed in the thermostat, a tool for maintaining steady temperature. Thermostats are employed in electric laundry irons, immersion heaters for hot water tanks, refrigerators and air-conditioners.

Expansion of Liquids:

Dissimilar gases, liquids expand at various rates, based on their composition. Liquids as well expand by various amounts at different temperatures. How much a volume of a given liquid will expand as its temperature increases from one degree to the subsequent can be found out by experiment or - in case of numerous common liquids - through consulting tables. The expansion of liquids via heat (and loss of volume if heat is reduced) is employed in thermometers. The expansion of freezing water can cause rock and masonry to break, and will as well crack plumbing pipes and engine blocks; precautions against their freezing are thus very vital.

Apparent and Real Expansion of Liquids:

A liquid is heated while keeping it in a vessel. There takes place an expansion of the solid vessel all along with the liquid. However the amount of expansion of the container is small as compared to that of the liquid. Therefore the expansion of a container is not generally noticeable.

- If the expansion of liquid is considered avoiding the expansion of the vessel, it is termed as apparent expansion.

- The real expansion of liquid is computed through adding the expansion of the part of the container having liquid (before expansion) by means of the apparent expansion of liquid.

Anomalous Expansion of Water:

We are familiar from the foregoing that most of the liquids expand if heated and contract whenever cooled. Water is the exception to this rule as it behaves in an anomalous manner when cooled. It contracts on cooling from a higher temperature till the temperature falls to 4oC. At 4oC, it begins to expand if cooled further beneath this temperature to 0oC. That is water expands if cooled from 4oC to 0oC. As an outcome of this, a given mass of water consists of its least volume and its highest density at 4oC. This anomalous behavior of water is described in an experiment termed as Hope's experiment.

Importance of Anomalous Expansion of Water in Nature:

The anomalous expansion of water is significant to us as it makes lakes, ponds and rivers to freeze from the top surface instead of from the bottom. As an outcome, marine lives can survive throughout winter since ice forms at the surface of the water whereas the bottom of the lake remains at 4oC a temperature warm adequate for aquatic animals like fishes.

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