Thermal and Chemical Effects of Electric Current
Exercises, Q13 - Q24
13. The temperatures of the junctions of a bismuth silver thermocouple are maintained at 0°C and 0.001°C. Find the thermo-emf (Seebeck emf) developed. For bismuth-silver, a =-46x10⁻⁶ V/deg and b =-0.48x10⁻⁶ V/deg².
ANSWER: Thermo-emf of a thermocouple having one end 0°C and the other at θ is given as
Ɛ =aθ +½bθ²
=(-46x10⁻⁶)*0·001 +½(-0·48x10⁻⁶)*(0·001)²
=-4·6x10⁻⁸ -2·4x10⁻¹³ V
=-4·6x10⁻⁸ V.
{Since the 2nd term is negligible in comparison with the first term}.
14. Find the thermo-emf developed in a copper-silver thermocouple when the junctions are kept at 0°C and 40°C. Use the data in the table (33.1).
ANSWER: Here θ =40°C. From table (33.1),
acs =(2·76-2·50) µV/°C
=0·26 µV/°C
bcs =(0·012 -0·012) µV/(°C)² =0
Hence the thermo-emf of the given Copper-Silver thermocouple is
Ɛcs =acsθ +½bcsθ²
=0·26*40 µV
=10·4 µV
=1·04x10⁻⁵ V.
15. Find the neutral temperature and inversion temperature of copper-iron thermocouple if the reference junction is kept at 0°C. Use the data in the table (33.1).
ANSWER: When one end of a thermocouple is kept at 0°C and the temperature of the other end θ is varied then the neutral temperature is the value of θ for which the maximum thermo-emf is developed in the thermocouple. The neutral temperature is at
θ = -a/b
From table (33.1),
a =2·76 -16·6 = -13·84 µV/°C
and b =0·012 -(-0·030) µV/(°C)²
=0·042 µV/(°C)²
Hence the neutral temperature of the given thermocouple
= -(-13·84)/0·042 °C
=329·5°C
≈330°C.
Given the temperature of the cold junction
θ' =0°C
Neutral temperature, θ =329·5°C
Inversion temperature, θ" =?
We know the relation among these three temperatures is
θ -θ' = θ" -θ
→θ" =2θ -θ'
=2*329·5 -0 =659°C.
16. Find the charge required to flow through an electrolyte to liberate one atom of (a) a monovalent material and (b) divalent material.
ANSWER: (a) One atom of a monovalent material will require the charge of one electron to flow through the eletrolyte to liberate which is equal to
q =1·602x10⁻¹⁹ C
(b) Similarly, one atom of a divalent material will require the charge of two electrons to flow through the electrolyte to liberate which is equal to 2q.
2q =2*1·602x10⁻¹⁹ C
=3·204x10⁻¹⁹ C.
17. Find the amount of silver liberated at cathode if 0.500 A of current is passed through AgNO₃ electrolyte for 1 hour. The atomic weight of silver is 107·9 g/mole.
ANSWER: Since silver is monovalent, one mole of silver ion will require one mole of electrons to be liberated at the cathode. The charge of one mole of electrons is 1 faraday =96485 C. So 96485 C will liberate 107·9 g of silver which is gram-equivalent of silver.
The amount of charge flown through the electrolyte q =Current*time
→q =(0·500 A)*(1x3600 s)
=1800 C
Hence the amount of silver liberated at cathode =(107·9)*1800/96485 g
=2·01 g.
You may also put values directly into the formula, m =(1/K)EQ.
18. An electroplating unit plates 3·0 g of silver on a brass plate in 3·0 minutes. Find the current used by the unit. The electrochemical equivalent of silver is 1.12x10⁻⁶ kg/C.
ANSWER: Given, Z=1.12x10⁻⁶ kg/C,
m = 3·0 g =0.003 kg,
time t =3·0 minute =180 s.
If i is the current used, then
m =Zit
→0·003 =1·12x10⁻⁶*i*180
→i =0·003/(1·12x10⁻⁶*180) A
→i = 14·90 A ≈15 A
19. Find the time required to liberate 1·0 liter of hydrogen at STP in an electrolytic cell by a current of 5·0 A.
ANSWER: Given, i =5·0 A. One gram mole of an ideal gas occupies 22·4 liters of volume at STP. Hence 1·0 liter of hydrogen has 1/22·4 =0·0446 moles at STP. Mass of one mole of hydrogen =2 g because one molecule of hydrogen contains 2 atoms. The mass of 0·0446 moles of hydrogen, m =0·0446*2 g =8·892x10⁻⁵ kg.
E = chemical equivalent of hydrogen
=(relative atomic mass)/valency
=1/1 =1·0
Mass of the substance liberated,
m =EQ/K
→m =Eit/K
→t =mK/Ei
=(8·892x10⁻⁵)*9.6485x10⁷/(1·0*5·0) s
=1716 s
=1716/60 minutes
≈29 minutes.
20. Two voltameters, one having a solution of silver salt and the other of a trivalent-metal salt, are connected in series and a current of 2 A is maintained for 1·50 hours. It is found that 1·00 g of the trivalent metal is deposited. (a) What is the atomic weight of the trivalent metal? (b) How much silver is deposited during this period? The atomic weight of the silver is 107·9 g/mole.
ANSWER: The amount of charge passing through each voltameter is,
Q =it =2*1.5*3600 C
=10800 C.
(a) Let the atomic weight of the trivalent-metal =M.
Its Chemical equivalent, E =M/3,
Liberated mass, m =1 g =0·001 kg
m =EQ/K
→0·001 =(M/3)*10800/9.6485x10⁷
→M =3*96485/10800
= 26·8 g/mole.
(b) Valency of silver = 1, hence
E =107·9/1 =107·9 g
Silver deposited in this period,
=EQ/K
=107·9*10800/9·6485x10⁷ kg
=0·0121 kg
=12·1 g.
21. A brass plate having a surface area of 200 cm² on one side is electroplated with 0·10 mm thick silver layers on both sides using a 15 A current. Find the time taken to do the job. The specific gravity of silver is 10·5 and its atomic weight is 107·9 g/mol.
ANSWER: Volume of the electroplated silver,
=(2*200)*(0·10/10) cm³
=4 cm³.
Given that specific gravity of silver
=10·5
Hence its density =10·5 g/cm³
Thus the electroplated mass of silver,
m =4*10·5 g =42 g =0.042 kg
Valency of silver is 1, hence its chemical equivalent, E = 107·9/1 =107·9 g.
Let the time taken in this job = t seconds. Since the current i = 15 A,
Charge passed through the electrolyte,
Q =it =15t,
Now, m =EQ/K
→0·042 =107·9*15t/(9.6485x10⁷)
→t =0·042*9.6485x10⁷/(107·9*15)
=2504 s
=42 minutes.
22. Figure (33-E2) shows an electrolyte of AgCl through which a current is passed. It is observed that 2·68 g of silver is deposited in 10 minutes on the cathode. Find the heat developed in the 20 Ω resistor during this period. The atomic weight of silver is 107·9 g/mole. 
The figure for Q-22
ANSWER: We know, m =EQ/K,
→m =Eit/K,
→i =mK/Et.
We have, m =2.68 g =2.68x10⁻³ kg
K =9·6485x10⁷ C/kg,
For silver E =107·9/1 =107·9 g
t =10 minutes =600 s.
Hence current in the circuit,
i =(2.68x10⁻³*9.6485x10⁷)/(107·9*600) A
=4·0 A
So the heat developed in 20 Ω resistor during this period,
= i²Rt
=(4·0)²*20*600 J
=192000 J
=192 kJ.
23. The potential difference across the terminals of a battery of emf 12 V and internal resistance 2 Ω drops to 10 V when it is connected to a silver voltameter. Find the silver deposited at the cathode in half an hour. The atomic weight of silver is 107·9 g/mole.
ANSWER: Let the current in the circuit = i.
Since the internal resistance of the battery =2 Ω, and due to this the potential difference across the terminals drops by 2 V hence,
i*(2 Ω) =2 V,
→i =1 A.
Hence the silver deposited at the cathode in half an hour,
m =EQ/K
=107·9*(1 A*30*60 s)/(9·6485x10⁷) kg
=0·00201 kg
=2·01 g.
24. A plate of area 10 cm² is to be electroplated with copper (density 9000 kg/m³) to a thickness of 10 micrometers on both sides, using a cell of 12 V. Calculate the energy spent by the cell in the process of deposition. If this energy is used to heat 100 g of water, calculate the rise in the temperature of the water. ECE of copper =3x10⁻⁷ kg/C and specific heat capacity of water =4200 J/kg-K.
ANSWER: Volume of the copper deposited,
=(2*10/10000)*10x10⁻⁶ m³
=2x10⁻⁸ m³
Mass of the copper deposited,
m =2x10⁻⁸*9000 kg
=1·8x10⁻⁴ kg
Let the current supplied by the 12 V cell, =i, then
m =Zit
→it =m/Z
=1·8x10⁻⁴/(3x10⁻⁷) C
=600 C
Hence the energy spent by the cell,
=V*it
=12*600 J
=7200 J
=7·2 kJ.
If this energy is spent to heat 100 g (=0.10 kg) of water, the rise in temperature of the water,
=H/(ms)
=7200/(0·10*4200) K
≈17 K
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CHAPTER- 33- Thermal and Chemical Effects of Electric Current
CHAPTER- 32- Electric Current in ConductorsCHAPTER- 31- CapacitorsCHAPTER- 30- Gauss's Law
CHAPTER- 29- Electric Field and Potential
CHAPTER- 28- Heat Transfer
OBJECTIVE -I
CHAPTER- 26-Laws of Thermodynamics
CHAPTER- 25-CALORIMETRY
Questions for Short Answer
OBJECTIVE-I
OBJECTIVE-II
EXERCISES - Q-11 to Q-18
CHAPTER- 24-Kinetic Theory of Gases
CHAPTER- 23 - Heat and Temperature
CHAPTER- 21 - Speed of Light
CHAPTER- 20 - Dispersion and Spectra
CHAPTER- 19 - Optical Instruments
CHAPTER- 18 - Geometrical Optics
CHAPTER- 17 - Light Waves
CHAPTER- 16 - Sound Waves
CHAPTER- 15 - Wave Motion and Waves on a String
CHAPTER- 14 - Fluid Mechanics
CHAPTER- 13 - Fluid Mechanics
CHAPTER- 12 - Simple Harmonic Motion
CHAPTER- 11 - Gravitation
CHAPTER- 10 - Rotational Mechanics
CHAPTER- 9 - Center of Mass, Linear Momentum, Collision
CHAPTER- 33- Thermal and Chemical Effects of Electric Current
CHAPTER- 32- Electric Current in Conductors
CHAPTER- 31- Capacitors
CHAPTER- 30- Gauss's Law
CHAPTER- 29- Electric Field and Potential
CHAPTER- 28- Heat Transfer
CHAPTER- 26-Laws of Thermodynamics
CHAPTER- 25-CALORIMETRY
Questions for Short Answer
OBJECTIVE-I
OBJECTIVE-II
CHAPTER- 24-Kinetic Theory of Gases
CHAPTER- 23 - Heat and Temperature
CHAPTER- 21 - Speed of Light
CHAPTER- 20 - Dispersion and Spectra
CHAPTER- 19 - Optical Instruments
CHAPTER- 18 - Geometrical Optics
CHAPTER- 17 - Light Waves
CHAPTER- 16 - Sound Waves
CHAPTER- 15 - Wave Motion and Waves on a String
CHAPTER- 14 - Fluid Mechanics
CHAPTER- 13 - Fluid Mechanics
CHAPTER- 12 - Simple Harmonic Motion
CHAPTER- 11 - Gravitation
CHAPTER- 10 - Rotational Mechanics
CHAPTER- 9 - Center of Mass, Linear Momentum, Collision
CHAPTER- 8 - Work and Energy
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CHAPTER- 7 - Circular Motion
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CHAPTER- 6 - Friction
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CHAPTER- 5 - Newton's Laws of Motion
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CHAPTER- 4 - The Forces
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CHAPTER- 3 - Kinematics - Rest and Motion
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CHAPTER- 2 - "Physics and Mathematics"
CHAPTER- 2 - "Physics and Mathematics"
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