LESSON No. – 3

THERMODYNAMIC EQUILIBRIUM:

Equilibrium of a system refers to the situation in which it’s “state” does not undergo any change in itselfwith passage of time without the aid of any external agent. Equilibrium state of a system can be examinedby observing whether the change in state of the system occurs or not. If no change in state of systemoccurs then the system can be said in equilibrium. Thermodynamic equilibrium is a situation in whichthermodynamic system does not undergo any change in its state. Let us consider a steel glass full of hotmilk kept in open atmosphere. It is quite obvious that the heat from milk shall be continuously transferredto atmosphere till the temperature of milk, glass and atmosphere are not alike. During the transfer of heat from milk the temperature of milk could be seen to decrease continually. Temperature attains some finalvalue and does not change any more. This is the equilibrium state at which the properties stop showingany change in themselves.

Generally, thermodynamic equilibrium of a system may be ensured by ensuring the mechanical,thermal, chemical and electrical equilibriums of the system. ‘Mechanical equilibrium’ of the system canbe well understood from the principles of applied mechanics which say that the net force and momentshall be zero in case of such equilibrium. Thus, in the state of mechanical equilibrium the system doesnot have any tendency to change mechanical state as it is the state at which the applied forces anddeveloped stresses are fully balanced.

‘Thermal equilibrium’ is that equilibrium which can be stated to be achieved if there is absence ofany heat interactions. Thus, if the temperature states of the system do not change then thermal equilibriumis said to be attained. Equality of temperature of the two systems interacting with each other shall ensurethermal equilibrium.

‘Chemical equilibrium’ is the one which can be realized if the chemical potential of the systemsinteracting are same. The equality of forward rate of chemical reaction and backward rate of chemicalreaction can be taken as criterion for ensuring the chemical equilibrium. Similar to this, in case theelectrical potential of the systems interacting are same, the ‘electrical equilibrium’ is said be attained.

Thermodynamic equilibrium implies all those together.

A system in thermodynamic equilibrium does not deliver anything.

TEMPERATURE MEASUREMENT ZEROTH LAW OFTHERMODYNAMICS:

After the identification of ‘Temperature’ as a thermodynamic property for quantification of the energyinteractions the big question was its estimation. Based on the relative degree of coldness/hotness conceptit was concluded that the absolute value of temperature is difficult to be described. Hence it was mooted to make temperature estimations in reference to certain widely acceptable known thermal states of thesubstances. Temperature is thus the intensive parameter and requires reference states. These acceptableknown thermal states are such as the boiling point of water commonly called steam point, freezing pointof water commonly called ice point (0o C) etc.

The methodology adopted was to first develop a temperature measurement system which couldshow some change in its characteristics (property) due to heat interactions taking place with it. Suchsystems are called thermometers, the characteristics of property which shows change in its value istermed thermometric property and the substance which shows change in its thermometric property iscalled thermometric substance. Science that deals with the temperature and its measurement is calledthermometry. For example in case of clinical thermometer the mercury in glass is the thermometricsubstance and since there is change in length of mercury column due to the heat interactions taking placebetween the thermometer and the body whose temperature is to be measured, therefore the length is thethermometric property. Thus, the underlying principle of temperature measurement is to bring thethermometer in thermal equilibrium with the body whose temperature is to be measured, i.e. when thereis no heat interaction or the state when two (thermometer and body) attain same temperature. In thisprocess it is to be noted that thermometer is already caliberated using some standard reference points bybringing thermometer in thermal equilibrium with reference states of the substance.

Zeroth law of thermodynamicsstates that if the bodies A and B are in thermalequilibrium with a third body C separatelythen the two bodies A and B shall also be inthermal equilibrium with each other. This isthe principle of temperature measurement.Block diagram shown in Fig. 3.1a and 3.1bshow the zeroth law of thermodynamics andits application for temperature measurementrespectively.

Figure 3.1 Zeroth law of thermodynamics
Figure 3.2Application of Zeroth law for temperature measurement

TEMPERATURE SCALES:

Number of temperature measuring scales came up from time to time. The text ahead gives a brief ideaof the different temperature scales used in thermometry. Different temperature scales have differentnames based on the names of persons who originated them and have different numerical values assignedto the reference states.

(a) Celsius Scale or Centigrade Scale

Anders Celsius gave this Celsius or Centigrade scale using ice point of 0°C as the lower fixed point andsteam point of 100ºC as upper fixed point for developing the scale. It is denoted by letter C. Ice pointrefers to the temperature at which freezing of water takes place at standard atmospheric pressure.Steam point refers to the temperature of water at which its vaporization takes place at standard atmosphericpressure. The interval between the two fixed points was equally divided into 100 equal parts and eachpart represented 1ºC or 1 degree celsius.

(b) Fahrenheit Scale

Fahrenheit gave another temperature scale known as Fahrenheit scale and has the lower fixed point as32 F and the upper fixed point as 212 F. The interval between these two is equally divided into 180 part.It is denoted by letter F. Each part represents 1 F.

(c) Rankine Scale

Rankine scale was developed by William John MacQuorn Rankine, a Scottish engineer. It is denoted byletter R. It is related to Fahrenheit scale as given below.

TR = TF + 459.67

(d) Kelvin Scale

Kelvin scale proposed by Lord Kelvin is very commonly used in thermodynamic analysis. It also definesthe absolute zero temperature. Zero degree Kelvin or absolute zero temperature is taken as –273.15ºC. Itis denoted by letter K.

Mathematically, it is related to the different temperature scales as follows,

TEMPERATURE MEASUREMENT:

For measurement of temperature number of thermometers are available using different thermometricproperties of the thermometric substances. Length, volume, pressure, resistance, e.m.f. etc. are thecommonly used thermometric properties for thermometers. Different thermometers developed usingthese thermometric properties are given below.

(a)Liquid Thermometer

(b)Gas Thermometers

(c)Electrical resistance thermometer

(d)Thermoelectric Thermometer

THERMOMETER CALIBRATION:

  1. Ice Point Method

• Fill an insulated container, such as a wide mouth “thermos” bottle with a mixture of potable crushed ice and water.

• The container must have crushed ice throughout to provide an environment of 32°F, so you may have to pack more ice into the container during the process.

• When the mixture of the water has stabilized after four or five minutes, insert the thermometer to be calibrated to the appropriate immersion depth.

• Be sure to hold the stem of the instrument away from the bottom and sides of the container (preferably one inch) to avoid error.

• If your thermometer is not accurate within +/- 2°F of 32°F., adjust the thermometer accordingly.

The ice point method permits calibration to within 0.1°F

  1. Boiling Point Method

• After the water in the container has reached a complete “rolling” boil, insert the instrument to the appropriate immersion depth. The boiling point in Wisconsin is 212°F.

• Be sure there is at least a two-inch clearance between the stem or sensing element and the bottom and sides of the container.

• If your thermometer is not accurate within +/- 2°F of 212°F., adjust thermometer accordingly.

The boiling point method permits calibration to within 1.0°F.

Ice Point Method / Boiling Point Method

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