Thermal Properties of Matter

1. Concept of Heat and Temperature

Familiar sensations of hotness and coldness are described with adjectives such as hot, warm, cold, cool etc. So, the quantity that indicates how warm or cold an object is called TEMPERATURE. However you must note here that these physical sensations of warmth and cold are not reliable because they depends on contrast as explained in this observation.
OBSERVATION :-
Suppose if we place our right hand in hot water and left hand in cold water, if after a few minutes we place both the hands in water at room temperature then you will notice that to the right-hand water will appear to be cold and to left-hand, water will appear to be hot.
From the above observation we can conclude that assessing the temperature of a body by mere sense of touch or comparing the degree of hotness of a body with respect to another body does not help in measuring the temperature quantitatively and accurately.
Another observation about hot and cold bodies in contact is that, when they both are in contact, the temperature of cold body increases and that of the hot body decreases. This happens because energy is transferred from hot body to cold body when they are in contact and this is a non-mechanical process.

This energy which is transferred from one body to another without any mechanical work involved is known as HEAT. Heat is a form of energy and heat transfer from one body to another takes place by virtue of temperature difference only. Also heat transfer takes place from the body at higher temperature to a body at a lower temperature. So, we can also say that \textslHeat is energy in transit. On microscopic level heat energy possessed by a body is due to the kinetic energy of the molecules that makes up the body. Heat energy can change from one form to another. S.I. unit of heat is Joule (J) and SI unit of temperature is Kelvin (K).

2. Zeroth Law of Thermodynamics

This fundamental law states that
If two bodies A and B are separately in thermal equilibrium with the third body C , then A and B are in thermal equilibrium with each other.
Now, Thermal equilibrium between two systems is the condition under which two substances in physical contact with each other exchange no heat energy.
OBSERVATION:-
1. Suppose there are two bodies A and B and a third body C ( assume it to be a thermometer).
2. Consider two bodies A and B , isolated from from each other.
3. Now we want to know whether A and B are in thermal equilibrium with each other.
4. For this we would put body A in contact with body C (thermometer) till they both are in thermal equilibrium .
5. At that stage reading of thermometer will become constant.
6. Thermometer is now put in thermal contact with body B.
7. We will wait till it is in thermal equilibrium with body B and note the temperature.
8. If two readings are same, then A and B are thermal equilibrium with each other.
The concept of thermal equilibrium or Zeroth law gives us the concept of temperature. All bodies which are in thermal equilibrium have a common property whose value is the same for all the bodies. We call this property as temperature. Thus , the temperature is that property of a body by which we know whether the body is in thermal equilibrium with other given body , or not.
Thus from above discussion, temperature of a system can be defined as the property that determines whether the body is in thermal equilibrium with the neighboring systems. So, if a number of systems are in thermal equilibrium, then a common property of the system can be represented by a single numerical value called Temperature. So if two systems are not in thermal equilibrium then they are at different temperatures.

3. Measurement of temperature

Measurement of temperature of a body is very important. It is also necessary to be able to measure both high and low temperatures. To make this possible it is necessary to construct a suitable scale of temperature. The scale chosen must be precise and consistent. The temperatures measured on this scale must be accurate. Measurement of temperature can be obtained using a thermometer. A thermometer, such as mercury in glass thermometer, is a device whose readings depends on hotness or coldness of an object. A thermometer is a reliable device for measurement of temperature than our senses.
The temperature of an object is not a fixed number but depends on the type of thermometer and on the temperature scale adopted. Construction of thermometers generally requires a measurable property of a substance which monotonically changes with temperature. Examples of some common type of thermometers:
1. Mercury in a glass thermometer:- The height of mercury in the tube is taken as thermometric parameter.
2. Constant Volume gas thermometer:- Gas in bulb is maintained at constant volume. The mean pressure of gas is taken as thermometric parameter.
3. Constant Pressure gas thermometer:- Gas in bulb is maintained at constant pressure. Volume of gas is taken as thermometric parameter.
4. Resistance thermometer:- Electric resistance of a metal wire increases monotonically with the temperature and may be used to define temperature scale. Such thermometers are resistance thermometers. Electric resistance of metal wire increase monotonically with temperature and may be used to define the temperature scale. If $R_{0}$ and $R_{100}$ are resistance of metal wire at ice and steam point respectively then temperature t can be defined corresponding to resistance $R_{T}$ as follows $$T=\frac{(R_{T}-R_{0})100}{(R_{100}-R_{0})}$$ A platinum wire is often used to construct a thermometer which is known as platinum resistance thermometer.
Some other type of thermometers are radiation thermometers, bimetallic thermometers , magnetic thermometers etc. Thermometers are calibrated to assign a numerical value to any given temperature. Definition of any standard scale needs two fixed reference points and these points can be correlated to physical phenomenon reproducible at the same temperature. Two such standard points are freezing and boiling points of water at same pressure. Two such familiar scales used for measurement of temperature are Celsius and Fahrenheit scale. Temperature in Celsius is measured in degree. Fahrenheit scale has a smaller degree then Celsius scale and a different zero of temperature. Relation between Celsius and Fahrenheit scale is
$$T_{F}=\frac{9}{5}T_{C}+32^{\circ}$$ Where, $T_{F}$ temperature in Fahrenheit and $T_{C}$ – Temperature in Celsius.
Letters $C$ and $F$ are used to distinguish measurements on two scales thus, $0^{\circ}C=32^{\circ} F$ this means that $0^{\circ}$ C on Celsius scale measures the same temperature as $32^{\circ}$ F on the Fahrenheit scale. On Fahrenheit scale melting point of ice and boiling point of water have values $32^{\circ}F$ and $212^{\circ}F$ and that on Celsius scale are $0^{\circ} C$ and $100^{\circ} C$.
If we now talk of Kelvin scale ,the melting point of ice and boiling point of water in the scale are 273.15 K and 373.15 K respectively.Size of a degree in Celsius and kelvin scale are same. Relation between Celsius and kelvin scale is
$$T_{C} = T_{K} - 273.15 K$$ where, $T_{K}$ is Temperature in Kelvin and $T_{C}$ - Temperature in Celsius.

Above figure shows the temperatures of the absolute zero, meting point of ice and the boiling point of water as measured on the Celsius, Kelvin , Fahrenheit and Rankine scales. Celsius and Fahrenheit scales show the same reading at $-40{^0}$ that is $-40{^0}C=-40{^0}F$. The Kelvin scale and Rankine scale agree at zero degree only.
Relation
$$\frac{C-0}{100}=\frac{F-32}{180}=\frac{K-273}{100}=\frac{R-492}{180}$$ Also, $$\frac{K}{100}=\frac{R}{180}$$

Solved Examples

Question 1 The temperature of the surface of sun is about $6500^{0}C$. What is the temperature on (i) the Rankine scale and (ii) on the Kelvin Scale?
Solution Here $C=6500^{0}C$
We have the relation ,
\begin{align*} & \frac{C-0}{100}=\frac{K-273}{100}=\frac{R-492}{180} \end{align*} Putting the value of $C$ in above relation We get \begin{align*} & \frac{6500}{100}=\frac{K-273}{100}=\frac{R-492}{180} \\ & K=6500+273=6773 K \\ & R=12,192^{0}R \end{align*} The temperature of the surface of sun corresponding to $C=6500^{0}C$ is (i) $6773 K$ and (ii)$R=12,192^{0}R$