Physics 12th Thermal Effect of Current

Thermal Effect of Current

(1) Introduction

• We have already learned the electric current and the physics behind it in the previous chapter
• We have also discussed the mechanism of flow of current in a conducter but not the physical consquences of flow of elctric current are related to other forms of energy
• In this chapter we will study about causes and consequences of electric current
• In the nutshell ,what we will study in this chapter is the connection between the electricity and thermal energy.

(2) Heating effect of current

• In previous chapter while discussing electric energy and power ,we learned that IΔV amount of energy is lost per second when a current I flows through a potential ΔV and this energy appears in the form of heat energy
• Due to the conversion of electric energy into heat energy the conductor becomes hot .This effect is known as Joule's Heating and this heating is thermodynamics irreversible.Cause Behind Joule's Heating:-
• Explanation behind the Joule's heating is that when a potential difference ΔV is maintained between the ends of a conductor,the free electrons in the conductor are accelerated towards the higher potential end of the conductor
• In their way electrons frequently collided withe the positive ions of the conductor due to which their velocity decreased
• This the energy electrons gained on account of acceleration is transferred to the positive lattice ions or atoms and electrons then returns to their equilibrium distribution of velocities
• Thus ,lattice ions receives energy randomly at the average rate of IΔV per unit time
• Ions spends this energy by vibrating about their mean positions resulting in rise in the temperature of the conductor
• This way Joule's heating nothing but the conversion of electrical energy into heat energy

(3) Thermoelectricity

• We know that currents flows in a conductor whenever there is a electric potential difference betweens the ends of the conductor
• If there is a temperature difference between the ends of the conductor then thermal energy flows from hotter end to the colder ends
• Thermal energy flows may also be carries by the electrons in the conductor and hence resulting the presence of electric current
• At the hotter end of the conductor electrons have slightly higher kinetic energy and hence they move faster
• So there is net flow of current towards the end of the conductor with lower temperature.Thus an electric current exists in the conductor due to the difference in the temperature of two ends of the conductor
• This phenonmenon due to which electricity is produced when two ends of the conductor are kept at different temperature is known as thermoelectricty

(4)Seeback effect

• Seeback effect was first discovered by Thomas John seaback
• It stated that when two different conductor are joined to form a circuit and the two junctions are held at the different temperature then an emf is developed which results in the flow of the electric current through the circuit.Arrangement is shown as below in figure
• Maginitude of thermo-electric emf depends upon the nature of the two metals and on the temperature difference between terminals
  
  
• Seaback effect is reversible i.e, if the hot and cold junctions are reversed the direction of thermoelectric current is alse reversed
• Seaback investigated thermo-electric properties of a large number of metals and arranged them in a series known as thermo-electric series or seaback series and is given as follows
  Bi,Ni,Co,Pt,Cu,Mn,Hg,Pb,Sn,Au,Ag,Zn,Cd,Fe,As,Sb,Te
• When any two of these metals in the series is used to form a thermocouple ,the thermo emf is greater when two metals used are farther apart in the circuit
• Figure 1 shows the thermocouple of Cu and Fe.The current in this couple flows from Cu to Fe through the hot junction
• The thermo emf of this couple is only 1.3 milivolt for a temperature difference of 100 C between the hot and cold junction

(5) variation of thermo-emf with temperature

• To study the effect of difference of temperature of the two junctions consider a thermo-couple of two dis-similar metals A and B
• Now consider that cold junction is at temperature 0 C and the temperature of the hot junction is raised gradually
• It is found in experiment that thermo emf varies with the temperature of the hot junction
• Figure below shows the graph of variation of thermo emf in the circuit with the variation of temperature of the hot junction.
  
• From graph it is clear that thermoemf is zerp when both the junctions are at the same temperature 0 C and gradually increases as the temperature of the hot junction increases 
• The temperature of the hot junction at which thermoemf in the thermocouple becomes maximum is called neutral temperature (T_n) for that thermocouple
• For a given thermo-couple of two metals neutral temperature has a fixed value
• On further increasing the temperature of the hot junction,after T_n has reached,The thermo-emf decreases and becomes equal at a particular temperature called temperature of inversion T_i.
• Beyond T_i ,if the temperature of hot junction is still increased ,the thermo-emf again started to increase but in reverse direction
• Temperature of inversion T_i is as much above the neutral temperature as neutral temperature is above the temperature of the cold junction.Thus mathimatically
  T_n-T_c=T_i -T_n
  or T_n=(T_i+T_c)/2
  Hence neutral temperature is the mean of the temperature of inversion and temperature of the cold junction
• Thermo-emf is the property of each material and can be easily measured for a junction of two dissimilar metals at different temperatures
• Thermo-emf of number of thermocouples is given by the simple relation
  E=αT+βT²
  where T is the temperature difference between the two junction and α and β are the parameters of the materoal used
• Also the rate of change of thermo-emf with temperature i.e dE/dT is called thermo-power or seaback coefficent S .Mathematically
  S=dE/dT 

(6) Peltier Effect

• Peltier effect is named after his discover Jean Peltier who in 1934 discovered a thermo-electric effect which is converse of Seaback effect
• Peltier discovered that "when an electric current is passed through two disimilar conductor connected to form a thermo-couple ,heat is evolved at one junction and absorbed at the other end.The absorption and evolution of heat depends on the direction of flow of current
  
  
• Peltier effect is entirely reversible in nature
  
  Peltier Coefficent
• Peltier coefficent is defined as the amount of heat energy absorbed or evolved due to peltier effect at the junction of two dissimilar metals when one coulumb of charge passes through the junction
• Peltier coefficent is denoted by π
• Value of Peltier Coefficent is different for different thermo-couple .Its value also depends upon the temperature of the junction
• If q amount of charge passes through the junction then
  Energy absorbed or evolved=πq
  if V is the contact Potential difference
  Then workdone=qV
  Now heat absorbed=Workdone
  So π=V
• Hence Peltier coefficent (in J/C) at a junction is numerically equal to the contact v in(Volts)

(7) Thomson effect

• Thomson effect is related to the emf that develops between two parts of the single metal when they are at different temperature
• Thus thomson effect is the absorption or evolution of heat along a conductor when current passes through it when one end of the conductor is hot and another is cold
• If two parts of the metal are at small temperature difference dT ,themn the electric potential difference is proportional to dT dV α dT
  or
  dV=σdT
  where σ is the constant of proportinality and is known as thomson coefficent
• Peltier coefficent and thomson coeficent are related to thermopower according to following relations
  π=Ts=T(dE/dT)
  and σ =-T(ds/dT)=-T(d²E/dT²)
• We have seen that all the three effects are defined in terms of three coefficent namely seaback,peltier and thomson coefficent but the basic quantity is thermo-power which is the rate of change of thermo-emf with temperature

(8)Applications of thermoelectricity or thermo-electric effect are

• To measure temperature using thermo electric thermometer
• To detect heat radiation using thermopiles
• Thermoelectric refregerator or generator