Source: https://www.hcvermasolution.com/hc-verma-solutions-for-class-12-physics-chapter-33-thermal-and-chemical-effects-of-electric-current/
Timestamp: 2019-04-21 16:51:22+00:00

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If a constant potential difference is applied across a bulb, the current slightly decreases as time passes and then becomes constant. Explain.
i=VR. Now, the heat generated by the resistance is constantly radiated to the surroundings. Thus, the value of its temperature is maintained and hence its resistance. As a result, current through the bulb filament becomes constant.
Two unequal resistances, R1 and R2, are connected across two identical batteries of emf ε and internal resistance r (figure). Can the thermal energies developed in R1 and R2 be equal in a given time? If yes, what will be the condition?
For the given time t, let the currents passing through the resistance R1 and R2 be i1 and i2 , respectively.
When a current passes through a resistor, its temperature increases. Is it an adiabatic process?
No, the rise in the temperature of a resistor on passing current through it is not an adiabatic process. In an adiabatic process, there is no heat exchange between the system and the surroundings. Here, some part of Joule’s heat developed inside the resistor increases the temperature of the resistor and the remaining part is dissipated in the surroundings. Thus, the given process cannot be adiabatic.
Apply the first law of thermodynamics to a resistor carrying a current i. Identify which of the quantities âˆ†Q, âˆ†U and âˆ†W are zero, positive and negative.
The battery is doing positive work on a resistor carrying current i. Thus, âˆ†W is positive. The work done on the resistor is used to increase its thermal energy; thus âˆ†Q is positive. As the temperature of the resistor rises, âˆ†U is positive.
Do all thermocouples have a neutral temperature?
There will be no neutral or inversion temperature, as the temperature of the hot junction cannot be less than the temperature of the cold junction.
Is inversion temperature always double the neutral temperature? Does the unit of temperature have an effect in deciding this question?
If the inversion temperature and neutral temperature are measured in degree Celsius, then it is correct to say that “inversion temperature is always double the neutral temperature.” When temperature is measured in other units, such as Kelvin, then inversion temperature is not the double of neutral temperature.
Is neutral temperature always the arithmetic mean of the inversion temperature and the temperature of the cold junction? Does the unit of temperature have an effect in deciding this question?
No, the neutral temperature is not always the arithmetic mean of the inversion temperature and the temperature of the cold junction. That is valid only when the unit of temperature is degree Celsius.
Do the electrodes in an electrolytic cell have fixed polarity like a battery?
No, the electrodes in an electrolytic cell do not have fixed polarity like that of a battery. If we take an electrolytic cell consisting of the Ag electrodes and the AgNO3 as electrolyte. When the battery is connected to it, the end to which the positive terminal of the battery is connected is the anode and the end to which the negative terminal is connected is the cathode.
NO3-ions are deposited at the anode and Ag+ ions are deposited at the cathode. When the connection of the electrolytic cell is reversed, the polarities of the electrodes are also reversed.
As temperature increases, the viscosity of liquids decreases considerably. Will this decrease the resistance of an electrolyte as the temperature increases?
Yes, the resistance of the electrolyte will decrease with an increase in temperature. This is because when the temperature of an electrolytic solution increases, its viscosity decreases and mobility of the ions in the solution increases.
Which of the following plots may represent the thermal energy produced in a resistor in a given time as a function of the electric current?
Plot (a) is the correct option.
This relation shows that the heat produced for a given time in a resistor varies with the square of current flowing through it. Hence, the plot between H vs I should be a parabola symmetric along the H axis, which is represented by curve a.
A constant current i is passed through a resistor. Taking the temperature coefficient of resistance into account, indicate which of the plots shown in the figure best represents the rate of production of thermal energy in the resistor.
When current passes through a resistor, the temperature of the resistor increases due to the heat produced in it.
dUdtalso increases linearly, which is best represented by plot d.
Consider the following statements regarding a thermocouple.
(A) The neutral temperature does not depend on the temperature of the cold junction.
(B) The inversion temperature does not depend on the temperature of the cold junction.
The value of neutral temperature is constant for a thermocouple. It depends on the nature of materials and is independent of the temperature of the cold junction. Inversion temperature depends on the temperature of the cold junction, as well as the nature of the material.
The heat developed in a system is proportional to the current through it.
(a) It cannot be Thomson heat.
(b) It cannot be Peltier heat.
(c) It cannot be Joule heat.
(d) It can be any of the three heats mentioned above.
Joule heat is directly proportional to the square of the current passing through the resistor. Peltier heat is directly proportional to the current passing through the junction.Thomson heat is also directly proportional to the current passing through the section of the wire. Thus, the heat developed can be either Thomson heat or Peltier heat. But it cannot be Joule heat.
(A) Free-electron density is different in different metals.
(B) Free-electron density in a metal depends on temperature.
In Seebeck Effect, a temperature difference between two dissimilar electrical conductors produces a potential difference across the junctions of the two different metals. The cause of this potential difference is the diffusion of free electrons from a high electron-density region to a low electron-density region. The free electron-density of the electrons is different in different metals and changes with change in temperature. Hence, both the statements are the causes of Seebeck Effect.
In Peltier Effect, one of the junctions gets heated up and the other cools down when electric current is maintained in a circuit of material consisting of two dissimilar conductors.
This is caused due to the difference in density of free electrons in different metals. When two different metals are joined to form a junction, the electrons tend to diffuse from the side with higher concentration to the side with lower concentration. If current is forced through the junction, positive or negative work is done on the charge carriers, depending on the direction of the current. Accordingly, thermal energy is either produced or absorbed. Thus, Peltier Effect is caused due to A but not due to B.
If a metallic conductor has non-uniform temperature distribution along its length, the density of the free electrons is different for different sections. The electrons diffuse from the sections with higher concentration to those with lower concentration of free electrons. Thus, there is an emf inside the metal that is known as Thomson emf. If a current is forced through the given conductor, positive and negative work is done on the charge carriers, depending on the direction of current. Thus, thermal energy is either produced or absorbed. Thus, the correct cause of the given effect is given by statement B alone.
Faraday,s constant is a universal constant. Its value is 9.6845×107 C/kg. It does not depend on the amount of the electrolyte, current in the electrolyte and on the amount of charge passed through the electrolyte.
As the resistors are in series, the current through them will be same. Thus, the amount of thermal energy produced in the resistors is same. The rise in the temperature of the resistance will depend on the shape and size of the resistor. Thus, the rise in the temperature of the two resistances may be equal.
The copper strip AB and an iron strip AC are joined at A and the junction A is maintained at 0°C and the free ends B and C are maintained at 100°C. In this case, there will be generation of thermo-emf between the points that are at different temperatures. Here, the two ends of the copper, the copper end and the iron end at the junction, the two ends of the iron strip and the free ends B and C are at different temperatures. Hence, there will be potential difference among them.
θn=-ab,the neutral temperature will be less than the temperature of the cold junction of thermocouple.
Hence, there will be no neutral or inversion temperature, as the temperature of the hot junction cannot be less than the temperature of the cold junction.
An electrolysis experiment is stopped and the battery terminals are reversed.
(a) The electrolysis will stop.
(b) The rate of liberation of material at the electrodes will increase.
(c) The rate of liberation of material will remain the same.
(d) Heat will be produced at a greater rate.
In an electrolytic cell, both the electrodes are made of the same material. Thus, on reversing the terminals of the battery, the direction of the flow of charges will be reversed, but the rate of the electrolysis will remain the same.
The electrochemical equivalent of a substance is the ratio of the relative atomic mass of the substance to its valency. Thus, it is only dependent on the nature of the material.
An electric current of 2.0 A passes through a wire of resistance 25 Ω. How much heat will be developed in 1 minute?
A coil of resistance 100 Ω is connected across a battery of emf 6.0 V. Assume that the heat developed in the coil is used to raise its temperature. If the heat capacity of the coil is 4.0 J K−1, how long will it take to raise the temperature of the coil by 15°C?
H=V2RtThis heat produced is used to increase the temperature of the coil.
The specification on a heater coil is 250 V, 500 W. Calculate the resistance of the coil. What will be the resistance of a coil of 1000 W to operate at the same voltage?
Let R be the resistance of the coil.
A heater coil is to be constructed with a nichrome wire (ρ = 1.0 × 10−6 Ωm) that can operate at 500 W when connected to a 250 V supply. (a) What would be the resistance of the coil? (b) If the cross-sectional area of the wire is 0.5 mm2, what length of the wire will be needed? (c) If the radius of each turn is 4.0 mm, how many turns will be there in the coil?
(a) Let R be the resistance of the coil.
An electric bulb, when connected across a power supply of 220 V, consumes a power of 60 W. If the supply drops to 180 V, what will be the power consumed? If the supply is suddenly increased to 240 V, what will be the power consumed?
R=V2P=220×22060=806.67 Ω(a) Now the supply drops to V’ = 180 V.
A servo voltage stabiliser restricts the voltage output to 220 V ± 1%. If an electric bulb rated at 220 V, 100 W is connected to it, what will be the minimum and maximum power consumed by it?
An electric bulb marked 220 V, 100 W will get fused if it is made to consume 150 W or more. What voltage fluctuation will the bulb withstand?
Given that the operating voltage is V and power consumed is P.
v=pR=150×484 =269.4 V=270 VThe bulb will withstand up to 270 V.
An immersion heater rated 1000 W, 220 V is used to heat 0.01 m3 of water. Assuming that the power is supplied at 220 V and 60% of the power supplied is used to heat the water, how long will it take to increase the temperature of the water from 15°C to 40°C?
An electric kettle used to prepare tea, takes 2 minutes to boil 4 cups of water (1 cup contains 200 cc of water) if the room temperature is 25°C. (a) If the cost of power consumption is Re 1.00 per unit (1 unit = 1000 watt-hour), calculate the cost of boiling 4 cups of water. (b) What will be the corresponding cost if the room temperature drops to 5°C?
1000 watt – hour = 1000 × 3600 watt sec.
The coil of an electric bulb takes 40 watts to start glowing. If more than 40 W are supplied, 60% of the extra power is converted into light and the remaining into heat. The bulb consumes 100 W at 220 V. Find the percentage drop in the light intensity at a point if the supply voltage changes from 220 V to 200 V.
Case-I : When the supply voltage is 220 V.
Case-II : When the supply voltage is 200 V.
The 2.0 Ω resistor shown in the figure is dipped into a calorimeter containing water. The heat capacity of the calorimeter together with water is 2000 J K−1. (a) If the circuit is active for 15 minutes, what would be the rise in the temperature of the water? (b) Suppose the 6.0 Ω resistor gets burnt. What would be the rise in the temperature of the water in the next 15 minutes?
⇒H=95×95×2×15×60=5832 JThe heat capacity of the calorimeter together with water is 2000 J K−1. Thus, 2000 J of heat raise the temp by 1 K.
2000 J raise the temperature by 1 K.
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 = − 46 × 10−6 V°C−1 and b = −0.48 × 10−6 V°C−2.
b = − 0.48 × 10−5 V °C−2.
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 table (33.1).
Find the neutral temperature and inversion temperature of a copper-iron thermocouple if the reference junction is kept at 0°C. Use the data in the table (33.1).
Find the charge required to flow through an electrolyte to liberate one atom of (a) a monovalent material and (b) a divalent material.
Find the amount of silver liberated at the cathode if 0.500 A of current is passed through an AgNO3 electrolyte for 1 hour. Atomic weight of silver is 107.9 g mol−1.
So, 2.01 g of silver is liberated.
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 1.12 × 10−6 kg C−1.
Find the time required to liberate 1.0 litre of hydrogen at STP in an electrolytic cell by a current of 5.0 A.
Let the required time be t.
Two voltameters, one with a solution of silver salt and the other with 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? Atomic weight of silver is 107.9 g mol−1.
A brass plate of surface area 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−1.
The figure 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. Atomic weight of silver is 107.9 g mol−1.
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. Atomic weight of silver is 107.9 g mol−1.
Let i be the current through the circuit.

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