Concept of Temperature and Heat:

The concept of temperature is one of the basic concepts in physics. Temperature is estimated through the indirect method. Qualitatively, temperature of the body is degree of hotness or coldness of the body.  Temperature and heat are not same phenomenon. Temperature is the estimation of intensity or degree of hotness in the body. Technically, it is found by getting average speed of the body's molecules. Heat is the measure of quantity of heat energy present in the body. Spatial distribution of temperature in the body determines heat flow. Heat always flows from warmer to colder areas.

Heat held in the object depends not only on the temperature but also its mass. For instance, let us compare the heating of two different masses of water. In this example, one mass has a weight of 5 grams, while the other is 25 grams. If the temperature of both masses is raised from 20 to 25° Celsius, the larger mass of water will require five times more heat energy for this increase in temperature. This larger mass would also contain 5 times more stored heat energy.

Heat is total energy of molecular motion in the substance whereas temperature is the measure of average energy of molecular motion in the substance. Heat energy depends on speed of particles, the number of particles (size or mass), and the kind of particles in the object. Temperature doesn't depend on size or kind of object. For instance, temperature of the small cup of water might be same as temperature of the large tub of water, but tub of water has more heat as it has more water and therefore more total thermal energy.

Thermal Equilibrium:

Two bodies may be at different temperature - one hot and other cold. Hot one is said to have more heat energy than colder body. In another sense, temperature of the hot body is higher than the colder body. Though, if two bodies are now in contact with each other, heat energy flows from hot body to cold body until the temperatures of the two bodies are same. Two bodies are then explained as being in thermal equilibrium with each other. Hence, the thermal equilibrium exists between two bodies when they are in thermal contact with each other and there is no net flow of heat between them. It is a temperature of a body which finds direction of flow of heat from that body to another. It will flow until two temperatures are same that is there is thermal equilibrium. Once, there is thermal equilibrium between two bodies, and then it signifies that two temperatures are th same - no net flow.

The Zeroth Law of Temperature:

The zeroth law of thermodynamics assists us to compute concept of temperature objectively. Quantitative definition of temperature comprises terms of operations which should be independent of our sense perceptions of hotness or coldness. I.e., temperature has to be compute objectively and not subjectively.

It has been seen that there are some systems in which the measurable property of system differs with hotness or coldness of system.

 For instance:

i) Length L of mercury column in thin tube will change variation in temperature.

ii) Pressure P of constant volume container, estimated by the pressure gauge or a manometer

iii) The electrical resistance (R) of a wire that differs with hotness or coldness as with platinum resistance.

iv) Electromotive force (E) of the thermo-junction differs also with hotness or coldness of system

In thermodynamics, bodies are brought in contact to establish common temperature using one of the coordinates. Two bodies may be in direct contact or they may be separated by two kinds of wall. The kinds of wall are that is adiabatic and diathermic walls. Adiabatic walls are those through which no heat can be transmitted while walls through which heat can be transmitted are called as diathermic walls. In thermodynamics, these two words are utilized to explain the procedure of thermal equilibrium i.e., of being at thermal equilibrium.

The Zeroth Law:

Consider two systems A and B separated from each other by the adiabatic wall but every system is in contact with the third system C separated through the diathermic wall. Consider whole systems surrounded by the adiabatic wall. This is to make sure that no heat energy is lost to or gained from surrounding. Experiments have illustrated that systems A and B will get the thermal equilibrium with C. If though adiabatic wall is replaced by the diathermic wall. Instead of permitting both systems A and B to come to equilibrium with C at same time, we can first have equilibrium between A and C and then equilibrium between B and C ensuring that state of C is same in both cases, then A and B are brought in contact through the diathermic wall, they will be found to be in thermal equilibrium. It means that no further changes takes place in systems A and B.

Systems A and B are already in equilibrium with each other. Above principle is known as zeroth law of thermodynamics. Zeroth law of thermodynamics defines that: Two thermodynamics systems A and B are separately in thermal equilibrium with the third system C, then systems A and B are in Thermal equilibrium with each other. It is known as zeroth law as the most significant principles of thermodynamics have hitherto been recognized as the first, second and third laws of thermodynamics. It is the property known as temperature which determines whether or not given two systems are in thermal equilibrium. Temperature of the system is that property which determines whether or not it will be in thermal equilibrium with other system when two or more systems are in thermal equilibrium, they are said to have same temperature. If two systems aren't in thermal equilibrium, their temperatures should be different. The zeroth law is therefore utilized in establishing temperature of the body quantitatively and objectively. But before it is estimated, a scale should be established with the help of a physical property that differs with temperature -thermometer.

Scale of Temperature:

There are some principles underlying establishment of temperature scales. These principles are based on fact that when temperature of the body changes, all magnitudes of almost all its physical properties also change. Condition, of course, is that the variation of properties should be linear, i.e., uniform. Hence any property of any substance which differs uniformly with temperature can be utilized. Variation of one of the properties is selected to represent accompanying change of temperature. To estimate temperature, hence, we require selecting a physical property or parameter of the chosen substance which differs uniformly with temperature. The parameter or property is the variable that is assigned a constant value during the discussion or event. Some of the examples of the parameters are:

i) The volume of the liquid;

ii) The volume of the gas at constant pressure; (

iii) Pressure of a gas at constant volume;

iv) Electrical resistance of the conductor;

v) emf change of the thermocouple when there is a temperature difference between junctions of the thermoelectric thermometer.

For establishment of temperature scale, the following are needed:

(a) Specification of fixed points;

(b) Specification of method of interpolation.

Specification of Fixed Points:

Fixed points are temperatures chosen that are fixed and reproducible. They are helpful as reference temperatures. Changes in parameters from fixed points are assigned numbers known as degrees on the calibrated scale. Two such fixed points are:

i) The Lower fixed point (ice point): That is the temperature of equilibrium between ice, water and air saturated at standard pressure. This temperature is) 0^oC.

ii) Upper fixed point (steam point): That is the temperature of steam rising from pure water boiling under standard atmospheric pressure, i.e., the temperature of one standard atmosphere. This temperature is 100^oC.

iii) Fundamental interval: This is the difference between upper fixed point and Lower fixed point divided in equal parts. Other fixed points like sulphur point also exist for reference.

Factors for Changes in Fixed Points:

i) Changes in atmospheric pressure and latitude cause variation in freezing and boiling points. Changes caused by pressure in freezing point can be ignored. That because of impurities can't be ignored.

ii) Freezing point depression and Boiling point elevation are caused by impurities of slats. Therefore water utilized in determining the points is needed to be pure.

iii) Daily floatation of barometric reading call for correction of boiling point. In neighborhood of standard atmospheric pressure, boiling point rises by 0.37^oC when height of mercury barometer increases by 1.0 cm. Thus true boiling point is provided as on Celsius scales as:

6^oC = 100^oC + 0.37 (B - 76)^oC

Where B is any atmospheric pressure in cm of mercury.

Temperature Scales:

 The systems of temperature scales are:

i) Celsius scales whose ice point is 0^oC and steam point is at 100^oC. Each part represents 1^oC.

ii) Fahrenheit scale whose ice point is 32^oF while steam point if 212^oF. Fundamental interval is 180 divisions. Each division represents 10^oF.

iii) Absolute scale of temperature, thermodynamics scale.

Specification of Interpolation:

The way we establish temperature of the body on either Celsius scale or Fahrenheit scale is what we refer to as specification of interpolation. This hence establishes scale of temperature that decides on temperature below, between and above fixed points, are to be established. We then select a thermometric substance and particular property that will serve as temperature indicator.

Definition of Temperature on Celsius Scale:

If X represents property of thermometric substance that acts as temperature indicator, by adopting Celsius scale. Let X_o be values of X of thermometric substance when surrounds by melting ice for the long time. Let X₁₀₀ be value of X when substance has reached the equilibrium with steam at standard pressure (1 atmosphere). Therefore, fundamental interval is stated as change of X between ice and steam points = X₁₀₀ - X_o.

Consequently, size of Celsius degree that results from choice of property X, is defined at that range of temperature that causes the change in property that is Z.

Therefore Z = (X₁₀₀ - X_o)/ 100..............................E.q.1

If X_t is the value of X of substance in neighborhood of another body whose temperature is to be determined then, number of degrees by which Celsius temperature t_c of thermometric substance exceeds temperature of melting ice 0^oC is equal to number of items the quantity Z is contained in (Xt - Xo).

Therefore (t_c - 0^oC) x Z = (X_t - X₀ )^oC..............................E.q.2

As Z = (X₁₀₀ - X_o)/100 Substituting Eq.1 in Eq.2, we get

(t_c - 0) x (X₁₀₀ - X_o)/100 = (X_t - X_o )^oC 100

Therefore t_c  = [(X_t - X₀ ) X 100^oC]/(X₁₀₀ - X_o) ..............................E.q.3

Definition of Temperature on Fahrenheit Scale:

In the case of the Fahrenheit scale, one can also define that

(t_F - 32) Z = (X_t - X₃₂)^oF ..............................E.q.4

Where, Z = [(X₂₁₂ - X₃₂)/(212 - 32)] ^oF

Z = (X₂₁₂ - X₃₂)/180 ^oF..............................E.q.5

Substituting Eq.4 in Eq.5, we get the expression

Therefore t_F - 32 = [(X_t - X₃₂)/(X₂₁₂ - X₃₂) x 180]^oF

Therefore t_F = [(X_t - X₃₂)/(X₂₁₂ - X₃₂) x 180 + 32]^oF..............................E.q.6

In addition, value of property of X at any definite temperature e is independent of method of numbering temperature.

Therefore X₂₁₂ = X₁₀₀ and X₃₂ = X_o

Now inserting the parameters in Eq.6, we get

t_F = [(X_t - X₀)/(X₁₀₀ - X₀) x 180 + 32]⁰F..............................E.q.7

Also from eq.3 we get

t_c/100 = (X_t - X₀)/(X₁₀₀ - X₀) ..............................E.q.7

Therefore, a relation between t_F and t_c can be obtained as

t_f = [t_c/100 x 180 + 32]⁰F

Therefore t_F = (9/5t_c + 32)⁰F..............................E.q.8

The Eq.8 allows us to convert the temperature measurement from one scale to other.

Thermodynamic Scale (Absolute Scale) of Temperature:

The thermodynamic scale is standard temperature scale utilized in scientific measurements. Symbol on this scale is T and it is measure in Kelvin after Lord Kelvin. On thermodynamic scale, the reference point is the triple point of water where saturated water vapor, pure water and melting ice are in equilibrium to each other. Temperature of triple point of water has been found to be 273.16K. Ice point is 273.15K. Minor difference with triple point is because of pressure in two cases. There is variation of Pressure (P) with temperature T. When graph is extrapolated, it meets temperature axis at -273.15^oC. This value of temperature is known as absolute zero (ok) by Kelvin. It is to be noted that value of pressure at this temperature decrease to zero.

On Celsius temperature scale,

-273.15^oC = 0

0^oC = 273.15K

Therefore the change in 1^oC on Celsius scale is equal to change of 1K on the Kelvin (Thermodynamics) scale.

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