Transmission of heat Questions and Answers

In thermal radiation of two black bodies the wavelengths corresponding to maximum emittance are in 2 3 proportion The ratio of areas of curves of spectral emissive power of bodies verses wavelength is A 3 2 B 81 16 C 9 4 D 27 8

A rigid insulated box is divided into two parts with a partition One part is occupied by 1 gm mole of ideal gas at temperature T and the other by 2 gm moles of the same ideal gas at temperature T2 When the partition is removed what is the final equilibrium temperature of the mixture Question Type Single Correct Type 1 T 2 T 3 T T T 2 2T T 3 T 2T 3

A block of metal is heated to a temperature much higher than the room temperature and allowed to cool in a room free from air currents Which of the following curves correctly represents the rate of cooling Question Type Single Correct Type 1 Temp 2 Temp 3 Temp Time Time Time

perat equall cold or hot The temperatures of block of wood and block of metal are Equal to temperature of the body Less than the temperature of the body Greater than temperature of the body Either 2 or 3

A piece of charcoal and a piece of shining steel of the same area are kept for a lon time in an open lawn in bright sun A the steel will absorb more heat than the charcoal B the temperature of the steel will be higher than that of the charcoal e if both are picked by bare hands the steel will be felt hotter than charcoal D if the two are picked up from the lawn and kept in a cold chamber the charcoal will lose heat at a faster rate than the steel

A spherical black body with radius of 10 cm radiates 500 W power at 400 K If temperature is doubled and radius is halved then power radiated in watt will be 500 250 2000

the layer A is a 50K b 12 5K c 25 K d 60 K 24 Which of the following statements is are false about mode of heat transfer a In radiation heat is transfered from one medium to another without affecting the intervening medium b Radiation and convection are possible in vaccum while conduction requires material medium Conduction is possible in solids while convection occurs in liquids and gases c d All are correct 25 In a vertical U tube containing a liquid the two arms are maintained at 9 30 12 sec as sho they ar ii the heat in a 2 Consis mater conduc conduc a

Boiling 3 A sphere made of aluminium alloy 2024 with a diameter of 20 mm and a uniform temperature of 500 C is suddenly immersed in a saturated water bath maintained at atmospheric pressure The surface of the sphere has an emissivity of 0 25 Calculate the total heat transfer coefficient for the initial condition What fraction of the total coefficient is contributed by radiation Answers h 180 W m K fraction 6 7

Heat is removed from a molten metal of mass 2 kg at a constant rate of 10 kW till it is completely solidified The cooling curve is shown in the figure 1100 1000 0s 1023K Temperature K 900 800 10s 873 K 700 600 500 0 0 20s 873 K testbok 30 s 600 K 10 20 30 40 Time S Assuming uniform temperature throughout the volume of the metal during solidification the latent host of fusion of the motal in

Four rods of same material with different radii r and length 1 are used to connect two heat reservoirs at different temperatures In which of following case heat conduction is fastest 1 1 1 r cm 1 cm 2 r 3cm 1 9cm 3 r 4cm 1 8cm 4 r 1cm 11cm

onsider a compound slab consisting of two different material having ual thickness and thermal conductivities k and 3k respectively as own in figure The equivalent thermal conductivity of the slab is e e 3k k 3k 2

A refrigerator converts 100 g of water at 25 C into ice at 10 C in one hour and 50 minutes The quantity of heat removed per minute is specific heat of ice 0 5 cal g C latent heat of fusion 80 cal g 50 cal O 100 cal O 200 cal O 75 cal

139 A black metal foil is warmed by radiation from a small sphere at temperature T and at a distance d where surrounding temperature is T It is found that the power received by the foil is P If both the temperature and the distance are doubled the power received by the foil will be Assume T Tol 1 16P 2 4P

4 The temperatures on the four surfaces of a very long square prism with dimensions w H 1 meter are given in the figure Find the temperature distribution T x y inside the bar at steady state 4 44 H lm oc 60 sin oc W lm 40sin T X

83 If a carved black utensil is heated to high temperature and then brought in dark then 1 Both utensil and its carving will shine 2 Only carving will shine 3 Only utensil will shine 4 None of the utensil and carving will shine

In Newton s law of cooling k40 the dt proportionality constant k is k and k for two substances A and B having mass m and m2 area A and A2 specific heat s and s2 emissivity e and e2 respectively it is given that 2 while 5 remains constant Then e e A B 1 C m2 surrounding temperature 3 9 A A 2 1 111 3

s I A container with 1 kg of water in it is kept in sunlight which causes the water to get warmer than the surroundings The average energy per unit time per unit area received due to the sunlight is 700 Wm and it is absorbed by the water over an effective area of 0 05 m Assuming that the heat loss from the water to the surroundings is governed by Newton s law of cooling the difference in C in the temperature of water and the surroundings after a long time will be Ignore effect of the container and take constant for Newton s law of cooling 0 001 s Heat capacity of water 4200 J kg K 8 33 P 700 x 0 05 35 watts P Pr 35 eGA4T0 AT 4eGAT K mC 4eGATO 0 001 x mC 4 2 from equation 1 AT 3 0 0001 35 50 25 6 3 8 33 1

15 f the temperature of the sun becomes twice its present temperature then Radiated energy would be predominantly in infrared Radiated energy would be predominantly in ultraviolet Radiated energy would be predominantly in X ray region Radiated energy would become twice the present radiated energy

Toluene liquid of volume 300 cm at 0 C is contained in a beaker and another quantiy of toluene of volume 110 cm at 100 C is in another beaker The combined volume is 410 cm Determine the total volume of the mixture of the toluene liquids when they are mixed together Given the coefficient of volume expansion a 0 001 C and all forms of heat losses can be ignored

far from the hotter end Also calculate the temperature gradient Three conducting rods of same material and cross section are shown in figure Temperature of A D and C are maintained at 20 C 90 C and 0 C Find the ratio of length BD and BC if there is no heat flow in AB A B 20 C 90 C D C 0 C

1 2 Abody cools according to Newton s Law of cooling The temperature of the body cools from 0 to 0 in time t The temperature of surrounding is 0 Find the time taken for the temperature of the body to decrease from 0 to 0 0 2 3

33 A steel plate is 0 3 m long 0 1 m wide and 0 012 m thick The plate is placed on a heating plate of identical size maintained at 100 C The heating plate is receiving energy through a 50 W heater The heating plate losses heat only to the steel plate which is well insulated from all sides except at the top The top surface of the steel plate is exposed to an airstream of temperature 20 C The top surface of the steel plate radiates like a black body Calculate the rate at which the top surface looses heat due to convection The surface of steel plate in contact with heating plate is at 100 C Thermal conductivity of steel k 16 Wm K Stefan s constant 5 67 x 10 8 Wm K 4 0 3 m 0 012 m 0 1 m Heating plate

We have noticed that some cooking pots have copper coating on bottom This is due to Low thermal conductivity of copper Copper retains heat than cooking pot Copper promotes distribution of heat over bottom of pot for uniform cooking Copper is not easily blackened

1 40cm 2 30cm 3 32cm 4 24cm 15 Steam is passed into 54g of water at 30 C till the temperature of the mixture becomes 90 C If the latent heat of steam is 536 cal g the mass of the mixture will be nearly 1 80g 2 60g 3 50g 4 24g A string of length 2x is stretched by 0 1x and the velocity of a transverse wave along it is v When it is 16

A vessel contains 100 g of water The heat capacity of the vessel is equal to 10 g of water The initial temperature of water in vessel is 10 C If 220 g of hot water at 70 C is poured in the vessel the final temperature neglecting radiation loss will be O 70 C O 80 C 60 C 50 C Marks 4 1

a 3 43 c 5 43 b 4 43 d 2 43 9 Three metal rods of the same material and identical in all respects are joined as shown in the figure The oc temperatures at the ends are maintained as indicated 90 C 90 C Assuming no loss of heat from the curved surfaces of the rods the temperature at the junction X would be d 20 C a 45 C b 60 C c 30 C

A liquid of mass m and specific heat C is at temperature 2T Another liquid of mass and m 2 specific heat 2C is at temperature T If these two liquids are mixed the resulting temperature of mixture is Question Type Single Correct Type 1 2 2 3 8 Ic T T

If Qamount of heat is required to increase the temperature of one mole of a monoatomic gas at constant pressure by AT the amount of heat required to increase the temperature of half mole of a diatomic gas at constant volume by 24T will be Q 5 3 Q 8Q 3 5 Q SOLUTION SR

Calculate the heat transfer from inner layers of the skin to the outer layer of the skin having the thickness of 1 cm and surface area of 1 5 m Consider the skin temperature as 34 C and the temperature of the body under normal conditions as 37 C a 90 J s b 150 J s c 128 J s d 156 J s

10 A spherical planet of radius r painted black travels around the sun in a circular orbit at a distance D from its centre r D The sun a sphere of radius R radiates as a blackbody at a temperature To 6000 K and subtends an angle 0 01 rad as seen from the planet The equilibrium temperature T of the planet is x x 100 Find x

In Newton s law of cooling dt proportionality constant k is k and k for two and area m substances A and B having mass m A and A specific heats and s emissivity and respectively it is given that m m 1 3 1 3 2 remains constant Then 2 1 1 S2 3 k2 2 4 219 e e2 while surrounding temperature 10 0 3 4 1 A A2 1

5 An ideal black body at room temperature is thrown into a furnace It is observed that 2002 2M a initially it is the darkest body and at later times the brightest b it is the darkest body at all times c it cannot be distinguished at all times d initially it is the darkest body and at later times it cannot he distinguished

a 2 0 s b 3 0 9 Three very large plates of same area are kept parallel and close to each other They are considered as ideal black surfaces and have very high thermal conductivity The first and third plates are maintained at temperatures 27 and 37 respectively The temperature of the middle i e second plate under steady state condition is 2012 a c 65 2 1 97 4 2 T T b 1 97 4 4 T d 97 4 T

A heat source inside a box A heat generating source S of power 36 cal sec is kept inside a thermally insulated box On two opposite walls of box there are two plugs P and P as shown in figure which are made of material having thermal conductivitiy 0 5 cal sec K cm and thickness 8cm and cross sectional area 12cm2 Find the steady state temperature inside the box if outside steady temperature are 100 C and 4 C at P and P respectively 100 C Heat source inside a insulating box S Pls answer few of my doubts here 1 What is the path of heat flow here From P1 to P2 Is it through the material of the box or the the space where Source S is placed 2 Also How can the temperature of inner surface be same as for conduction temperature difference is required 3 The key point in this question which I sto Yout

4 Temperature difference of 120 C is maintained between two ends of a uniform rod AB of length 2L Another bent rod PQ of same cross section as AB and length 3L is connected 2 across AB see figure In steady state temperature difference between P and Q will be close to 2019 Main 9 Jan I a 45 c 75 C A 4 P b 35 C d 60 C B

Objective Only one correct option 1 Two materials having coefficients of thermal conductivity 3K and K and thickness d and 3d respectively are joined to form a slab as shown in the figure The temperatures of the outer surfaces are 0 and 0 respectively 0 0 The temperature at the interface is d 3d K a 0 0 2 b 02 3K 01 20 2 3 3 c 0 0 2019 Main 9 April II 902 0 d 50 6 6 10 10

O A composite spherical shell is made up of two materials having thermal conductivities K and 2 k respectively as shown in the diagram The temperature at the innermost surface is maintained at T whereas the temperature at the outermost surface is maintained at 10 T A B C and D are four points in the outer material such that AB BC CD The effective thermal resistance between the inner surface of the shell and the outer surface of the shell for the radial heat flow is 10T 1 7 8 KR 7 KR 487 KR In the certain process 100 Cal of boot are supplic 1 2 3 4 6 49 KR 1000 tom and at the come time

19 Two rods of same material have same length and area The heat AQ flows through them for 12 minutes when they are joint side by side If now both the rods are joined in parallel then the same amount of heat AQ will flow in a 24 min c 12 min b 3 min d 6 min

What is the coefficient of performance of an ideal heat pump that extracts heat from 7 0 C air outside and deposits heat inside a house at 22 C Express your answer to two significant figures and include the appropriate units COP Submit Part B VAZO Request Answer If this heat pump operates on 1100 W of electrical power what is the maximum heat it can deliver into the house each hour Express your answer to two significant figures and include the appropriate units A www

A metal plate 4 mm thick has a temperature difference of 32 C between its faces It transmits 200 kcal h through ar area of 5 cm Thermal conductivity of the material is 58 33 W m 1 C 1 33 58 W m C 1 O 5x 10 4 W m 1 C 1 O None of these

49 A liquid initially at 70 C cools to 55 C in 5 min and 45 C in 10 min What is the temperature of the surroundings a 22 C b 21 C c 30 C d 25 C 50 A tub of hot water

at te of 9 17 14 17 cm d 3 17 5 17 cm c 9 17 18 17 cm 20 A copper rod 2 m long has a circular cross section of radius 1 cm One end is kept at 100 C and the other at 0 C and the surface is insulated so that negligible heat is lost through the surface Thermal conductivity of copper is 401 W m K Find the thermal resistance of the bar a 15 9 K W b 20 9 K W c 40 9 K W d 50 9 K W

7 A 42 kg block of ice moving on rough horizontal surface stops due to friction after sometime If the initial velocity of the decelerating block is 4 ms the mass of ice in kg that has melted due to the heat generated by the friction is Latent heat of ice is 3 36 x 105 1 km

a C spectra of a black body at temperatures 273 C and 546 C are shown in the figure If A and A be the areas A2 is under the two curves respectively the value of A 81 16 27 8 E b 16 1 d 546 C 16 81 273 C

a 1 b 1 2 c 2 3 1923 d 1 3 7 Two holes of unequal diameters d and d d d are cut in a metal sheet If the sheet is heated a Both d and d will decrease b Both d and d will increase c d will increase d will decrease d d will decrease d will increase

Three identical bodies are at temperature T T and T having e e and e as their respective emissivities The thermal spectrum obtained for them is as shown in the diagram Choose the correct order of temperatures and emissivities E II T M A 2 T T T O I 1 T e e e e e B T3

a P b E 2 c 4P d 2P 14 How much heat energy in joules must be supplied to 14g of N at room temperature to raise its temperature by 40 C at constant pressure a 50R b 60R c 70R d 80R

d Heating air around a furnace 2 Three discs A B and C having radii 2 m 4 m and 6 m respectively are coated with carbon black on their outer surfaces The wavelengths corresponding to maximum intensity are 300 nm 400 nm and 500 nm respectively The power radiated by them are Q4 QB and Qc respectively 2004 2M a Q is maximum c Qc is maximum b QB is maximum d 2A 2B Qc

A spherical object which behaves as a black body is raised to the temperature T and placed in an environment initially at o c While the object cools from T to the temperature T in an interval of time t t the environment rises to the temperature 1 C during the same time The average rate of cooling of the object dT and the average rate net to dt dT are respectively given by a and 0 B while the dt heat loss Q of the object during the time interval 0 same quantities during the interval 4 t are a and 0 B Read the following statement about this system State which of the above statements are true by correct choice from below 3T dT 4 dt E a B Ba a a B B The newton s law of cooling will be more accurate near then near 1 0 or 1 T The rate of cooling decreases with time at first reaches a minimum and then increases with time

are 13 Two identical conducting rods first connected independently to two vessels one containing water at 100 C and the other containing ice at 0 C In the second case the rods are joined end to end and connected to the same vessels Let q and 92 gram per second be the rate of melting of ice in the two cases respectively The ratio 1 is 2004 2M 92 a 1 b 4 c 1 d Y b