Transmission of heat Questions and Answers

Four identical rods which have thermal insulated lateral surfaces are joined at point O Points A B C and D are connected to furnaces maintained constant temperatures If the heat flows into the junction O from A at the rate of 2J s and from B at 4J s and flows out towards C at 8J s Choo the correct relation s B A O D C OA TA To B To Tc OC TA TD

A stationary object at 4 C and weighing 3 5 kg falls from a height of 2000m on a snow mountain 0 C If the temperature of the object just before hitting the snow is 0 C and the object comes to re immediately then the object will melt use g 10ms and latent heat of ice 3 5 10 J kg 1 2kg of ice 2 200 g of ice 3 20 g ice 4 2 g of ice In rainy season on a clear night the black seat of a bicycle becomes wet because 2 Black seat is good absorber of heat 1 It absorbs water vapour 2 Black coat in mod radiator of boot oparou 4 Mone of the abor

1 To the Window An ice factory as expected is quite chilly and must maintain an inside temperature of 25 Degrees F On a day like today the average temperature outside is 50 Degrees F Find the change in temperature in Kelvin One 3 m by 5 m window has a thickness of 0 5 cm If the thermal conductivity of glass is 0 75 J m s K how much heat gets transferred into the ice factory in a day

The rods of identical cross section and lengths are made of three different materials of thermal conductivity K K and K3 respectively They are joined together at their ends to make a long rod see figure One end ofr the long rod is maintained at 100 C and the other at 0 C see figure If the joints of the rod are at 70 C and 20 C in steady state and there is no loss of energy from the surface of the rod the correct relationship between K K and K3 is 100 C K K K3 0 C

Two metallic spheres S and S are made of the same material and have got the identical surface finish The mass of S is thrice that of S Both the spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other The ratio of the initial rate of cooling of S to that of S2 is A 1 3 B D 2017 1 3 O 3 1 1 3

Problem 1 Radiation sensor Hot part 0 5 m x 2 m 4 m Problem 1 The top surface of a 5mm thick nodized aluminum plate is suddenly irradiated with G 1000 W m2 while being simultaneously xposed to cooling airflow at a velocity of 10 m s nd T 30 C The bottom surface of the plate is nsulated and the plate is 1 2 m long in the flow lirection For a plate temperature of 400 K as well s 0 14 and 0 76 determine the radiosity at he top plate surface the net radiation heat flux at he top surface and the rate at which the

A concerned mother is dressing her child for play in the snow The child s skin temperature is 34 degrees Celsius and the outside air temperature is 1 5 degrees Celsius If the emissivity of the child s skin is 0 710 and has 0 0115 m of exposed skin area what is the amount of energy transferred from his body to the surroundings in 1 00 hr 1 4838 J 5342 J 2 3 J 4326 3J

4 A black body at 327 C suspended in a black enclosure at 27 C cools at certain rate If temperature of black body is lowered to t C so that rate of cooling becomes half of initial value then find approximate value of f in C 1 129 C 2 239 C 3 429 C 4 512 C COC in 5 minute th

4 A parallel plate capacitor is filled by a dielectric whose permittivity varies with the applied voltage according to the laws at where a IV The same but containing no dielectric capacitor charged sto a voltage U 156V is connected in parallel to the first nonlinear uncharged capacitor Determine the final voltage U across the capacitors l The capacitance of the nonlinear capacitor is

Two cylinders of same diameter one of silver and other of aluminium are placed in contact as shown in the figure If the thermal conductivity of silver is K and K that of aluminium is then the effective thermal 5 conductivity of the composite cylinder in steady state is A 200 C Ag K X 4 K x m 3 Al B 0 C

3 SA SB 6 Assume that Solar constant is 1 4 kW m radius of sun is 7 x 105 km and the distance of earth from centre of sun is 1 5 x 108 km Stefan s constant is 5 67 x 10 8 Wm 2 K4 find the approximate temperature of sun 1 5800 K 3 15500 K 2 16000 K 4 8000 K

Three identical conducting rods are joined as shown in the figure Points A and B are maintained at temperatures 300 C and 60 C respectively The temperature of the junction C will be F A 80 C 220 C 180 C 120 C B

What is the minimum volume of water at a temperature of 40 oC that is necessary to completely melt a 1 kg block of ice that has a temperature of 40 oC the interaction of ice and water with the external environment is neglected Give the volume in liters L The specific heat of water is 4190 J kg x K The latent heat of fusion of water passage from ice to water is 334 000 J kg The density of water is 1 kg liter The specific heat of ice is 2100 J kg x K

A black body with initial temperature of 300 C is allowed to cool inside an evacuated enclosure surrounded by melting ice at the rate of 0 35 C s If the mass specific heat and surface area of the body are 32g 0 1 c g s and 8x10 2 m calculate the Stefan s constant

45 Two bodies A and B of equal masses area and emissivity cooling under Newton s law of cooling from same temperature are represented by the graph If 0 is the instantaneous temperature of the body and 0 is the temperature of surroundings then relationship between their specific heats is 1 SA SB 2 log 0 0 A B t 2 S Sg luow SB A

A cyclic process for 1 mole of an ideal gas is shown in figure in the V T diagram The work done in AB BC and CA respectively Question Type Single Correct Type 1 A B T 0 RT en V R T T V 2 R T T 0 RT en 12 30 RT en V R T T BTaln B ToT

Q14 A composite bar made up of aluminium and steel is rigidly attached to the end supports at 60 C as shown in figure Find the stresses in the two portions of the bar when the temperature of the composite bar falls to 20 C if i the ends do not yield ii the ends yield by 0 25 mm Es 200 GPa EAI 70 GPa as 11 7 x 10 C CAI 23 4 x 10 C cross sectional areas As 250mm AAI 375mm Al 400 mm STEEL 800 mm

A composite slab is prepared by a pasting two plates of thickness L 2 m and L 1 m and the thermal conductivities k and k The slabs have equal cross section area Find the equivalent conductivity of the slab keq O keq 3k k 2k k 2k k k 2k1 3k kg keq 2k1 Okeg Okeq 3ky k 2kg 2k

A planet is at a distance r from the sun and its surfac temperature is constant at T Assuming that the plane receives energy only from the sun and loses energy only through radiation from its surface Neglecting atmospheric effects which of the following is correct for temperature T Tx r Txr 2 Tar 2 Tar 2

Two ends of a conducting rod of varying cross sections are maintained at 200 C and 0 C respectively In steady state B CD 0 C 200 C 1 temperature difference across AB and CD are equal 2 temperature difference across AB is greater than that of across CD 3 temperature difference across AB is less than that of across CD 4 temperature difference may be equal or different depending on the thermal conductivity of the rod

A wire of length 1 m and radius 10 3 m is carrying a heavy current and is assumed to radiate as a black body At equilibrium its temperature is 900 K while that of the surroundings is 300 K The resistivity of the material of the wire at 300 K is x10 8 m and its temperature coefficient of resistance is 7 8x10 3 per C Stefan s constant 5 68x10 8 W m K4 So the current in the wire is 310 1 25 A 3 21 A 2 15 A 4 36 A

1 22 C 3 25 C 2 26 C 4 32 C Air outside a water lake is blowing at 40 C It takes 10 hours for first two centimeter of ice layer to form over the lake Time taken to form next four centimeter of ice layer formation will be 1 20 hours 2 40 hours 3 60 hours 4 80 hours A hot solid metal ball of radius R is left for cooling artional 1

A rod 1 m long and made of material of thermal conductivity 420 W m K has one of its ends in melting ice and the other end in boiling water If its area of cross section is 10 cm2 the amount of ice that melts in 1 minute is Latent heat of fusion of ice 80 cal g 1 cal 4 2 J O 0 125 g O 75 g O 7 5 g O 450 g

5 Graphs give the temperature along an x axis that extends directly through a wall consisting of three layers with different nonzero and finite coefficient of thermal conductivities The air temperature on both sides of the wall are different and uniform Out of the situations as shown by the graphs which is are impossible TA TA a c TA 1 1 A B C A B C X X b d TA 1 1 ABC A B C

Consider two hot bodies B and B2 which have temperature 70 C and 60 C respectively at time t 0 The temperature of the surrounding is 40 C The ratio of the respective rates of cooling R and R of these two bodies at t 0 will be Question Type Single Correct Type 1 R R 3 2 2 R R 5 4 3 R R 2 3 4 R R 4 5

Three rods of same material same area of cross section but different lengths 10 cm 20 cm and 30 cm are connected at a point as shown What is temperature of junction O 20 C 1 19 2 C 3 11 5 C 30 cm 30 C 20 cm 10 cm 10 C 2 16 4 C 4 22 C

Two different metal slabs of identical length are joined in parallel Their cross sectional areas are A and 24 If their thermal conductivity coefficients are k and k as shown then their equivalent conductivity for one dimensional steady state heat transfer is Heat Flow 1 K K 2 3 2k k A 2A k K 2 k K k 2k 4

3 A cube and a sphere made of same material shown in figure are allowed to cool under identical conditions then 10 cm 10 cm 1 Cube will cool at a faster rate 2 Sphere will cool at a faster rate 3 Rate of cooling is independent of dimension of body 4 Both 2 and 3 are correct

3 Heat energy at constant rate is given to two substances P and Q If variation of temperature 7 of substances with time t is as shown in figure then select the correct statement TA P 1 Specific heat of P is greater than Q 2 Specific heat of Q is greater than P 3 Both have same specific heat 4 Data is insufficient to predict it

2 60 C 4 20 C 1 80 C 3 40 C 19 A cup of tea cools from 80 C to 79 9 C in 5 minute If temperature of surroundings is 20 C Then ho much time will it take to cool from 70 C to 69 9 Assume Newton s law of cooling is valid here 1 5 minute 2 6 minute 2 7 minute 4 8 minute

19 Liquid oxygen at 50 K is heated to 300 K at constant pressure of 1 atm The rate of heating is constant Which one of the following graphs represents the variation of temperature with time AIPMT Prelims 2012 mo 88 6 1 3 Temperature Temperature Time Time 2 4 Temperature Temperature Time ewoq ed Time

Heat flows radially outward through a spherical shell of outside radius R and inner radius R The temperature of inner surface is and that outer is At what radial distance fro m center of shell the temperature is just half way between and 0 B C R R 4R 3R 2 SR R 4R 3R A Correct Answer

28 Two coaxial cylinders of radius r and 3r are made of material of thermal conductivity K and K respectively The equivalent thermal conductivity of substance for axial heat flow may be 1 3 O K 4 K K 9 K 8K2 9 r 3r 2 4 K K 6K 9 K K2 2

Coefficient of thermal conductivity for three metals A B and C are such that K K K If same quantity of heat flow rate per unit area is obtained from each rod by providing a temperature gradient XX and X in A B and respectively then X X Xc O X XB Xc X X Xc o X X X X XB 2

Illustration 20 An ice box is built of wood 1 75 cm thick lined inside with cork 3 cm thick If the temperature of the inner surface of the cork is 0 C and that of the outer surface of wood is 12 C what is the temperature of the interface The thermal conductivity of wood and cork are 0 0006 and 0 00012 cgs units respectively

Illustration 21 Find the time in which a layer of ice 3 cm thick on the surface of a pond will increase its thicness by 1mm when the surrounding air is 20 C given Therma conductivity of ice 0 005 CGS units Latent heat of ice 80 cal g Density of ice at 0 C 0 91g cm

A spherical black body with a radius of 12 cm radiates 450 W power at 500 K If the radius were halved and the temperature doubled the power radiated in watt would be 1 225 3 900 2 450 4 1800

Illustration 18 The opposite faces of a metal plate of 0 2 cm thickness are at a difference of temperature of 100 C and the area of the plate is 200 sq cm Find the quantity of heat that will flow thorugh the plate in one minute if K 0 2 CGS units

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 QA QB and Qc respectively Then 1 QA is maximum 3 Qc is maximum 2 QB is maximum 4 Q Q 8

Two spheres of the same material have radii 1 m and 4 m temperatures 4000 K and 2000 K respectively Then the ratio of energy radiated per second by the first sphere as compared to that by the second is 1 4 1 3 1 1 2 2 1 4 1 4

1 Two spherical stars A and B emit blackbody radiation The radius of A is 400 times that of B and A emits 10 times the power emitted from B The ratio A of thei AB wavelengths A and Ag at which the peaks occur in the B respective radiation curves is

rod AB of uniform cross section consists of 4 sections AC CD DE and EB of different metals with thermal conductivities K 0 8 K 1 2 K and 1 50K respectively Their lengths are respectively L 1 2 L 1 5 L and 0 6 L They are joined rigidly in succession at C D and E to form the rod AB The end A is maintained at 100 C and the end B is maintained at 0 C The steady state temperatures of the joints C D and E are respectively Tc TD and Tp Column I lists the temperature differences TA Tc TCTD TD TE and TE TB in the four sections and Column II their values jumbled up Match each item in Column I with its correct value from Column II A C Column I p TA TC q Tc TD r TD TE s TE TB D E B Column II a 9 6 b 3 1 c 24 1 d 36 2

Pure water super cooled to 15 C is contained in a thermally insulated flask Small amount of ice is thrown into the flask The fraction of water frozen into ice is assume all water condenses as ice initially A 3 35 B 6 35 C 6 29 D 2 35 ant Academy I Pvt Ltd B 41 Road No 2 IPIA Kota Raj Ph 06377791915 www vibrantacademy com 15

Four rods of identical cross sectional area and made from the same metal form the sides of square The temperature of two diagonally points are T and 2T respectively in the steady state Assuming that only heat conduction takes place what will be the temperature difference between other two points 2 1 T 2 A C 0 2 B 2 1 D None of these T A C wh Sta 36 In bl th

A cylindrical volume of cross section area A and length contains a uniform mixture of three gases H2 02 and CO2 If their ratio by volume be 1 1 3 Find the time taken by sound to travel this length L if the temperature varies linearl from T 51 C to T 88 C across the length of cylindric volume

3 A black body is at a temperature of 2880 K The energy of radiation emitted by this object with wavelength between 250 nm to 255 nm is U between 500 nm to 505 nm is U and between 1500 nm to 1505 nm is U3 Then for this situation mark the correct statement 1 U U 0 3 U U L 2 U U 4 U can be zero

Three rods of the same cross section and made of the same material form the sides of a triangle ABC as shown The points A and B are maintained at temperatures T and 2 T respectively in the steady state Assuming that only heat conduction takes place the temperature at point C is A 1 2 2 3 2 3 B T 2 3 2 2 3 T 3 3 T 2 4

A cylinder with adiabatic walls contains water The cylinder is closed on top with a metal cover with area A thickness b thermal conductivity K Heat capacity of water is C temperature of surroundings is To assumed to be constant An electric heater produces heat at a rate H Find the temperature of water as function of time after the heater is switched on bi A To

A black body has maximum wavelength Am at 2000 K Its corresponding wavelength at 3000 K will be A 2 2 C E 16 81 Nill m 4 Am 3 B D Am 3 81 16 m Kerala P E T 2005

A metal ball of mass 0 1 kg is heated upto 500 C and dropped into a vessel of heat capacity 800 JK 1 and containing 0 5 kg water The initial temperature of water and vessel is 30 C What is the approximate percentage increment in the temperature of the water Specific heat capacities of water and metal are respectively 4200 JK and 400 J kg K JEE MAIN 2019 A 15 B 30 D 20 C 25