Joule's laws of heating
Work done by the electric field on the free electrons in time t is
W = potential difference * charge
= (iR)it = i²Rt
1. The heat produced in a given resistor in a given time is proportional to the square of the current in it, i.e.,
H α i²
2. The heat produced in a given resistor by a given current is proportional to the time for which the current exists in it, i.e.,
H α t
3. The heat produced in a given resistor by a given current in a given time is proportional to its resistance.
H α R
These three are known as Joule’s laws.
Verification of Joule’s laws
Done by Joules calorimeter.
K-oil is taken in a copper calorimeter, current i1 is sent for a time t and the rise in temperature (Δ θ1) is noted. Later on the oil is allowed to cool to the room temperature and current i2 is sent for a time of ‘t’ same as last time. The rise in temperature (θ2) is noted. (Δ θ2)
It can be found that
Δθ1/ Δθ2 = i1²/i2²
This shows that Δθ α i²
Verification of the law H α t is made by taking reading of rise in temperature at regular time intervals. It can be found that temperature rise in uniform in every time period. It increases by equal amount in equal time periods.
Verification of H α R is done by taking two joule calorimeters. Different resistances R1 and R2 are dipped in the K-oil of different calorimeters and the system is connected to a battery. The initial temperatures are noted and after some time the final temperatures arenoted. It can be seen that
Δθ1/ Δθ2 = R1/R2.
If the junctions of two metallic strips (joined at the ends to form a loop) are kept at different temeratures , there is an electric current in the loop.
This effect is called Seebeck effect and the emf developed is called the Seebeck emf and thermo emf.
This effect is reverse of Seebeck effect.
When the two junctions of a thermocouple (two different metallic strips joined at the ends to form a loop) are kept at the same temperature and electric current passed through them, it was observed that heat was produced at one junction and it was absorbed at the other junction. So one junction became hot and the other junction became cooler.
Metals are arranged in a series called thermoelectric series, which may be used to predict the direction of current in a thermocouple in the temperature range 0°C to 100°C.
Antimony, nichrome, iron, zinc, copper, gold, silver, lead, aluminium, mercury, platinum-rhodium, platinum, nickel, constantan, bismuth.
At the cold junction current is from the metal coming earliner in the series to the metal coming latter in the series. Furthre apart two metals lie in the series, larger is the emf produced.
Neutral and inversion temperature
The temperature of the hot junction at which the thermo emf is maximum is called the neutral temperature and the temperature at which the thermo emf changes its sign is called the inversion temperature.
If θc, θn, θi are temperature of the cold junction, neutral temperature and inversion temperature respectively
θn – θc = θi - θn
Sign convention in thermocouples
The thermo emf developed in a thermocouple of metals A and B denoted ЄAB is taken to be positive if the direction of the current is from A to B at the hot junction.
Thermo emf depends on temperature with the relation
ЄAB = aABθ + ½ bsub>ABθ²
Where aAB and bAB are constants for a pair of metals A and B.
This gives dЄAB/dθ = aAB + bsub>ABθ
The quantity dЄAB/dθ is called thermoelectric power at temperature θ.
The emf is maximum when dЄAB/dθ = 0, or θ = - aAB/ bAB. This is the neutral temperature.
At θ = - 2aAB/ bAB. The emf becomes zero. This is the inversion temperature.
Law of intermediate Metal
Suppose ЄAB, ЄAC, ЄBC are emfs from thermocoupes AB,AC, and BC.
If hot junctions and cold junctions of the three thermocouples are at the same temperature,
ЄAB = ЄAC - ЄBC
Law of intermediate temperature
Let Є θ1, θ2, represent the thermo-emf of a given thermocouple when the temperatures of junctions are maintained at θ1and θ2. Then
Є θ1, θ2 = Є θ1, θ3 + Є θ3, θ2
When current is passed through a metallic wire with non uniform temperature, it is observed that heat is absorbed in certain segments, and produced in certain segments. This heat is over and above i²Rt heat. This effect is given the name Thomson effect.
If a charge ΔQ is passed through a small section of the wire having a temperature difference ΔT between the ends, the Thomson heat is
ΔH = σ(ΔQ)( ΔT)
Where σ is a constant for a given metal at a given temperature.
The quantity ΔH/ΔQ = σΔT is called the Thomson emf.
σ is called the Thomson coefficient. It is taken as positive if heat is absorbed when a current is passed from the low temperature end to the high temperature end.
Copper, silver zinc, antimony, cadmium etc. have positive σ.
Iron, cobalt, nickel, bismuth, platinum etc. have negative σ. Negative sigma means, in these metal wires, heat is absorbed when current is passed from higher temperature end to the lower temperature end.
In lead, sigma is almost zero.
Explanation for Seebeck, Peltier and Thomson Effects
The density of free electrons is different in different metals. When two metals are joined to form a junction, the electrons tend to diffuse from the side with the higher concentration to the side with lower concentration. This produces a charge difference and hence an emf across the junction. This emf is the Peltier emf. When current is forced through this junction, positive or negative work is done the charge carriers, and due to the work thermal energy is produced or absorbed.
Similarly, when temperature of a metal piece is not uniform, density of free electrons varies inside the metal. The free electrons tend diffuse from the higher concentration regions to the lower concentration regions. This gives rise charge difference and hence an emf between the hot and cold parts of the metal. Hence when current is forced through this wire, positive or negative work is done and thermal energy is produced or absorbed. This is the Thomson effect.
In a thermocouple there are two junctions. If both a kept at the same temperature, Peltier emfs produced balance each other. If the junctions are at different temperatures, the emfs developed are different and there is a net emf in the loop. Also due to non uniform temperatures in the loop, Thomson effect is also present and Thomson emf is also produced. The actual emf produced in a thermocouple loop is the algebraic sum of the net Peltier effect and the net Thomspon effect.
So emf in a thermocouple loop = ЄAB =
(ΠAB)T - (Π AB ) T0 +(T – T0) (σA - σA)
(More explanation is needed for the formula.
(Not there in JEE Physics syllabus)
When a current passes through an electrolyte, chemical changes occur in the electrolyte and substances are liberated at the electrodes. This process is called electrolysis. A conducting liquid is called electrolyte. The vessel in which electrolyte is there and in which electrolysis takes place is called electrolytic cell.
When AgNO3 solution is put in an electrolytic cell, a fraction of the dissolved AgNO3 molecules are separated into two parts, Ag+
and NO3- ions. Each ion has electric charge positive or negative.
WWhen a battery is connected to the electrodes placed in the electrolytic cell, cations ( Ag+) move toward the cathode and anions move toward the anode. The ions give up the charge at the electrodes. Ag+ becomes Ag and gets deposited on the cathode.
NO3- ions go to anode and gives its extra electron to it. NO3 is formed and it reacts with the silver anode an forms AgNO3 and gets dissolved in the solution. This way, silver is contnously removed from the anode and deposited on the cathode with the concentration of the electrolyte remaining unchanged.
Electrolysis Faraday’s laws of electrolysis
1. The mass of a substance liberated at an electrode is proportional to the charge passing through the electrolyte.
2. the mass of a substance liberated at an electrode by a given maoutn of charge is proportional to the chemical equivalent of the substance.
Hence m α Q or m α it
M = Zit
Where Z is a constant for the substance being liberated. The constant Z is called the electrochemical equivalent (ECE) of a substance.
The SI unit of ECE is kilogram/coulomb written as kg/C
The chemical equivalent of a substance s equal to its relative atomic mass divided by its valency.
For silver relative atomic mass is 108 and its valency is 1 (Check silver’s atomic number and valency). Therefore, chemical equivalent of silver is 108 kg/C.