Transmission of heat Questions and Answers

Questions asked Prior to Medical Ent Exams 2005 27 The coefficients of linear expansion of brass and steel are a and a respectively When we take a brass rod of length 1 and steel rod of length 0 C then difference in their lengths 1 will remain the same at all temperatures if at 2 0 a

Data for Q No 83 to 84 A gas of N particles is enclosed in a volume V at a temperature T The logarithm of the partition function is given by In Z N In V bN kgT 3 2 where b is a constant with appropriate dimensions If P is the pressure of the gas the equation of state is given by a P V bN Nk T c P V b Nk T The interval energy of the gas is given by a U 1 2 k T c U 3 2 Nk T b P V bN k T d P V b Nk T b U Nk T d U 2Nk

Board Competitive Exams 14 When pressure remaining constant at what temperature will the r m s speed of a gas molecules increase by 10 of the r m s speed at NTP 1 57 3 K 3 557 3 K 2 57 3 C 4 57 3 C

3 3 x 10 c 4 Data is insufficient A metallic tape gives correct value at 25 C A piece of wood is being measured by this metallic tape at 10 C The reading is 30 cm on the tape the real length of wooden piece must be 1 30 cm 3 30 cm 2 30 cm 4 Data is not sufficient

Current is passed through a metallic wire heating it red When cold water is poured over half of its portion 1 Rest of the portion will become more hot 2 Rest of the portion will become cold 3 Whole rod will become cold

4 For larger ball is four times that of the other ball 40 A black body which is at a high temperature T K thermal radiation emitted at the rate of E W m If the temperature falls to 7 4 K the thermal radiation emitted in W m will be 1 E 2 E 4

Board Competitive Exams 41 A sphere a cube and a thin circular plate al made of the same mass and finish are heated to a temperature of 200 C Which of these objects wil cool slowest when left in air at room temperature 1 The sphere 2 The cube

A ferromagnetic material has a Curie temperature 100K Then a its susceptibility is doubled when it is cooled from 300K to 200K b all the atomic magnets in it get oriented in the same direction above 100K c the plot of inverse susceptibility versus temperature is linear with a slope To d the plot of its susceptibility versus temperature is linear with an intercent T

cup of coffee has a temperature of 80 C when it is poured and allowed to cool in a room with a temperature of 30 C After 1 minute the temperature of the coffee 5 C Determine the temperature of the coffee at time t How long must you wait until the coffee is 35 C 0 Jse integers or decimals for any numbers in the expression Round to four decimal places as needed

40 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 cooling 7 Temperature of block 3 time 2 time time Rash Educational Services Pvt Ltd Regd Office Aakash Tower 8 Pusa Road New Delhi 110005 Ph 011 47623456

A solid cylinder of radius 4 cm and length 50 cm emissivity 0 85 and temperature 127 C is radiating energy at rate P in surrounding at temperature 27 C If cylinder is stretched and new radius is 2 cm then energy transfer rate is P2 Then find P1 P2 A B C D 54 101 54 100 52 101 52 100 Correct Answer

12 For water at 0 C it takes one hour for first 3 mm of ice layer formation How much time will it take for next 6 mm of ice formation 1 2 hour 3 6 hour 2 4 hour 4 8 hour

Sirius A has a luminosity of 26 LSun and a surface temperature of about 9400 K Part A What is its radius Hint See Cosmic Calculations 12 2 Radius of a Star Express your answer using two significant figures V A O

35 If a metallic sphere gets cooled from 62 C to 50 C in 10 minutes and in the next 10 minutes gets com 42 C then the temperature of the surroundings is 1 30 C 3 26 C 2 4 36 C 20 C

6 Heat is flowing steadily from A to B 6 Temperature T at point P at distance x from A is such that A X 4 B 1 T decreases linearly with x 2 T increases linearly with x 3 T decreases exponentially with x 4 T increases with x as T a x AB A x A X 1 2 42 2 3 4 xa B

curve 128 For the following represents the total energy emitted by the perfect black body per second per unit area E over the complete wavelength range at that temperature 7 Thus area below the graph is in accordance with Symbols have usual meanings E 4 Ex T in m 1 Wien s displacement law 2 Stefan s law 3 Kirchhoff s law AY

3 0 5 3 Temperature difference between body and surroundings fall from 10 C to 5 C in 10 minutes Temperature difference between body and surroundings will fall from 5 C to 2 5 C in Use Newton s law of cooling 1 5 minutes Ta 10 minutes 2 20 minutes 4 Infinite

3 Melting 26 Q heat flows per second through the rod of length L and area of cross section A If it is stretched to double its length then what will be the heat flow per second keeping temperature difference same 1 2Q Q 4 3 2 2 4 Q

26 The temperature gradient in a rod of 0 5 m long is 80 C m If the temperature of hotter end of the rod is 30 C then the temperature of the colder end is 1 40 C 3 10 C The ratio 2 10 C 4 0 C

Q Q Two cylinders P and 2 of equal capacity are connected to each other via a stopcock Cylinder P contains an ideal gas at standard temperature and pressure Cylinder is completely evacuated The entire system is thermally insulated stopcock is suddenly opened What is the effect on internal energy of gas Increases O Decreases No change

K and K When points A and C are maintained at different temperature no heat flows through the central rod if ons are arranged as shown in the figure They have thermal conductivities K K Ky B 1 K K and K K 3 K K K K Convection A K K K 4 K C D 2 K K K K3 K K K K 2

34 Two steam engine A and B have their sources respectively at 700 K and 650 K and their sinks at 350 K and 300 K Then A A is more efficient than B B B is more efficient than A C both are equally efficient n depends on the fuels used in A B

8 A gas is compressed at a constant pressure of 50 Nm 3 3 from a volume of 10 m to a volume of 4 m Energy of 10 J then added to the gas by heating Its internal 50x6 lov energy is a increased by 400 J c increased by 100 J b increased by 200 J 300 3 decreased by 200 J

A thermally insulated cubical box of side length 20 cm and wall thickness 2 cm containing 2 kg of ice is closed on all sides The mass of ice melted in 10 hours is Thermal conductivity of the material of the box 0 01 Wm K latent heat of ice 360x103 J kg and ambient temperature 40 C 508 508 y 30 Jurbed Options 3 4 1 52 kg 1 25 kg 1 64 kg 20 cm 5065 2 cm Ke as goods 40 C 0 48 kg a 10 Kobe 8 So for song 0 01 Wm K 500 500 360 10 J kg 350 52 kg 70 107

O No 15 View In English Two sphores A and B have the same radi but the heat capacity of A is greater than that of B The surfaces of both are painted black They are heated to the same temperature and allowed to cool vacuum Then 1 3 4 Correct Answer 4 Your Answer 1 Status incorrect A cools faster than B both A and B cool at the same rate at any temperature the ratio of their rates of cooling is a constant B cools faster than A 4 V

Four rods of same material having same cross section length have been joined as shown in figure The temperature of the junction of four rods will be 0 C 90 1 Question Type Single Correct Type 20 C 2 30 C 30 C 3 45 C 60

Three concentric thin spherical shells are shown in figure Outer most sphere can t radiate in outer space The inner most and the outer most shells are maintained at T K T K respectively Assume the three shells behaves as black body The steady state temperature of the middle Value of x y is shell is T T X y 1 4 3R 2R

Two spherical black bodies made of same material and with the same surface finish have mass M and M and are at temperatures T and T If they are radiating the same power M M mu be 1 T T 6 2 T T 3 T T 6 4 T T

A highly conducting solid cylinder of radius a and length is surrounded by a co axial layer of a material having thermal conductivity K and negligible heat capacity Temperature of surrounding space outside the layer is T which is higher than the temperature of the cylinder If heat capacity per unit volume of the cylinder material is S and outer radius of the cylinder is b time required to increase the temperature of the cylinder from 7 to T is Assume end faces to be thermally insulated and given that b 2a T 500K T 300K T 400K In 2 0 7 Sa n 200K Where n

The resistance of the wire in platinum resistance thermometer at ice point is 3 2 and at steam point is 9 Q2 When the thermometer is inserted in an unknown hot bath its resistance is found to be 12 Q The temperature of the hot bath is A 100 C B 50 C C 75 C D 150 C

Find the true correct statements from the following During clear nights the temperature rises steadily upward near the ground level Two spheres of the same material have radii 1m and S and temperatures 4000 K and 2000 K respectively The energy radiated per second by the first sphere is greater than that radiated per second by the second sphere The total energy emitted by a black body per unit time per unit area is proportional to the square of its temperature in the Kelvin scale Newton s law of cooling an approximate form of Stefan s law is valid only for natural convection

Half part of ice block is covered with black cloth and rest half is covered with white cloth and then it is kept in sunlight After some time clothes are removed to see the melted ice Find the correct statement from the following Ice covered with black cloth will melt more Ice covered with white cloth will melt more Equal ice will melt under both clothes It will depend on the temperature of surroundings of ice

There is a rough black spot on a polished metallic plate It is heated upto 1400 K approximately and then at once taken in a dark room Th find true statement from the following The plate and the black spot can not be seen in the dark room The spot and the plate will be equally bright In comparison with the plate the spot will appear more black In comparison with the plate the spot will shine more

a 38 26 A square is made of four rods of same material one of the diagonal of a square is at temperature difference 100 C then the temperature difference of second diagonal 100 0 C d 100 C 2l b 100 l C

Q21 The spectrum of a black body at two temperatures 27 C and 327 C is shown in the figure Let A and A be the areas under the two curves respectively The value of A2 A is Intensity A 327 C 27 C Wavlength L a 1 16 b 4 1 c 2 1 d 16 1

A body cools from 60 C to 40 C in 10 minutes If the room temperature is 10 C and assuming Newton s cooling law holds good find the time taken to cools from 40 C to 20 C A B D 20 min 30 min 40 min 50 min

10 a Complete the sentences with words that describe the main process of thermal energy transfer in each case A man goes for a walk on a cold day He touches a metal gate which removes thermal energy from his hands by He holds the sides of a cup containing a hot drink His hands gain thermal energy by lit a fire The man warms his hands by the side of the fire His hands gain thermal energy by 3 b Describe in terms of particles the transfer of thermal energy through the metal of the gate after transfer from the man s hands Some farm workers have

A body at temperature 00 having Newton s cooling constant K is placed in a surrounding having temperature To at time t 0 The graph of temperature of the body as a function of time t is shown in the adjacent figure A tangent on the curve is drawn at t 0 as shown in the figure Find the value of T temp 1 K 2 1 K To Question Type Single Correct Type 3 K 00 To T time

The cylindrical filament of an incandescent lamp of power 64 W is made of Tungsten The operation temperature of the lamp is 2000K Consider the filament a black body and find its radius in mm Given o 6 10 8 W m length of 10 filament is 37 cm

Q2 A sphere of diameter D which is at a uniform temperature of T is suddenly removed from a furnace and suspended in a large room of air at uniform temperature of T There is a heat transfer by radiation determine the time taken by the sphere to cool to some temperature T k 200 W m K Cp 0 9 kJ kg K D 50mm T 800 k T 300 K T 400 K F 67x100 m K

An aluminum container of mass 100 gm contains 200 gm of ice at 20 C Heat is added to the system at the rate of 100 cal s The temperature of the system after 4 minutes will be specific heat of ice 0 5 and L 80 cal gm specific heat of A 0 2 cal gm C in C x x 8 1 Find x

6 Consider two hot bodies B1 and B2 which have temperatures 100 C and 80 C respectively at a time t 0 The temperature of surrounding is 40 C The ratio of the respective rates of cooling R1 R2 of these two bodies at that time will be O 3 2 O 2 3 O 5 4 O 4 5 1 point

6 Speed distribution of molecules of an ideal mono atomic gas trapped in a vessel is given in the following table Speeds of the molecules number of molecules 10 20 40 20 10 100 m s 400 m s 600 m s 800 m s 1000 m s of this gas is 324 K If all the molecules of speed 800 m s escape from the vessel by what amount will the temperature of the gas Temperature change a Increase by 47 C c Increase by 102 4 C A balloon filled with of 10 g of hydrogen b Decrease by 47 C d Decrease by 102 4 C

The earth receives on its surface radiation from the sun at the rate of 1400 W m 2 The distance of the centre of the sun from the surface of the earth is 1 5 10 m and the radius of the sun is 7 0 x 10 m Treating sun as a block body it follows from the above data that its surface temperature is A B C 5801 K 10 K 50 1 K 5801 C

28 6 The temperature of a cavity of fixed volume is doubled Which of the following is true for the black body radiation inside the cavity a its energy and the number of photons both increase 8 times b its energy increases 8 times and the number of photons increases 16 times c its energy increases 16 times and the number of photons increases 8 times d its energy and the number of photons both increase 16 times a P and Q

A quantity of heat Q is supplied to a monoatomic ideal gas which expands at constant pressure Th fraction of heat that goes into work done by the gas is fed ad fa t v cevi T QHEN GAR R 1 2 5 2 3 35 5 3 2 3 4 1

1 The coefficient of thermal conductivity of copper is nine times that of steel In the composite cylindrical bar shown in the figure what will be the temperature at the junction of copper and steel dia 3041 alcal quich zuld 3041 Alccal quis ga fax f ar n ziy nik 95 atau sud if i 114413 1 75 C 100 C 2 67 C 18cm copper iron 6cm 0 C 3 33 C 4 25 C

A hollow metallic sphere of radius 20 cm surrounds a concentric metallic sphere of radius 5 cm The space between the two spheres is filled with a nonmetallic material The inner and outer spheres are maintained at 50 C and 10 C respectively and it is found that 160 x Joule of heat passes radially from the inner sphere to the outer sphere per second Find the thermal conductivity of the material between the spheres

A body cools from 80 C to 70 C in 5 mins What wil be its temperature in the next 5 mins Temperature of surroundings is 10 C 7 kan 2 1 60 C 2 63 32 C alt 3 61 43 C 4 65 C 10 2K 75 10

1 kg of water at a temperature of 353 K is mixed adiabatically with an equal mass of water at 293 K Find the change in entropy of the universe assuming the specific heat of water to be constant equal to 238 J kg K