Transmission of heat Questions and Answers

Problem 1 50 points You are ready to boil pasta for dinner so you fill a 2 lb aluminum pot with roughly 1 2 L of water initially at 15 C and put it on the stove where the pot and water are heated until the water s about to start boiling You can assume that this process happens at atmospheric pressure 101 325 kPa a At what temperature is the water about to start boiling 10 points T b Neglecting any air in the pot being heated find the total amount of heat needed 20 points Q c For the water sketch the process in a P v diagram and a T v diagram making sure you show the saturation lines and the lines of constant temperature and pressure 20 points

22 The variation of temperature of a material as heat is given to it at a constant rate as shown in the figure The material is in solid state at the point O The state of the material at the point P is 1985 2M T A P C B Heat added D

Two rods of equal length and area of cross section are kept parallel and lagged between temperature 20 C and 80 C The ratio of the effective thermal conductivity to that of the first rod is K K 3 4 Question Type Single Correct Type 17 4 2 7 6 3 4 7

Consider a compound slab consisting of two different material having equal thickness and thermal conductivities k and 3k respectively as shown in figure The equivalent thermal conductivity of the slab is l l k 3k O O O 3k 2 4k 3

48 The inside and outside temperature of a refrigerator are 273K and 303 K respectively Assuming that refrigerator cycle is reversible for every joule of work done the heat delivered to the surrounding will be a 9J b 10J c 13J d 11J

The thickness of ice on surface of a lake becomes x cm and y cm starting from zero thickness in time t and to respectively If to 1 3 t 1 2 3 3 then 2 x y is equal

Two thin concentric shells made of copper with radius r and r r r have a material of thermal conductiv K filled between them The inner and outer spheres are maintained at temperatures T and To respective by keeping a heater of power P at the centre of the two spheres Find the value of P H C

Consider two insulating sheets with thermal resistances R R and R as shown The temperature 0 is 1 2 3 0 4 2 Question Type Single Correct Type R 0 0 R R R R 0 0 0 R 0 R R R 01 02 R R R R 2 0 R 0 R D 0 R 1

The two opposite faces of a cubical piece of iron Thermal conductivity 0 2 SI units are at 100 C in steam and 0 C in ice If the area of a surface is 4 m then the mass of ice melted in 10 minutes will be Approx Question Type Single Correct Type 1 35 g 2 300 g 3 7g

A black body is at a temperature of 2880 K The energy of radiation emitted by this object with wavelength between 499 nm and 500 nm is u between 999 nm and 1000 nm is u and between 1499 nm and 1500 nm is u3 The Wien constant is b 2 88 x 106 nm k Which of the following is correct A u 0 U U B u3 0 D U U

Calculate the rate of loss of heat through a glass window of area 1000 cm and thickness 0 4 c when temperature inside is 37 C and outside is 5 C Co efficient of thermal conductivity of gla 10 1 is 2 2 x 10 Cal s cm 2 3 Define co efficient of thermal conductivity and hence find its unit in SI A think ploce tumbler often cracks when boiling water is poured into it why

59 A system has non degenerate energy levels with energy E n 1 w where hw 8 625 10 5 eV and n 0 1 2 3 Calculate the probability that the system is in the n 10 state if it is in contact with a heat bath at room 300 K What will be the probability for the limiting cases of very low temperature and very high temperature temperature T

56 From observations on the intensities of lines in the optical spectrum of nitro gen in a flame the population of various vibrationally excited molecules rela tive to the ground state is found as follows V Ny No 0 1 000 1 0 210 2 0 043 3 0 009 Show that the gas is in thermodynamic equilibrium in the flame and calcu late the temperature of the gas 0 3 350 K

5 Assume the sun to be a black body at temperature 5800K The total ra diant energy emitted by the Sun per second and the solar energy reach ing Earth s atmosphere per second is o 5 672x10 8 SI unit radius of the Sun 7x108m distance of the Earth s atmosphere from the Sun 1 5x10 m Take T 3 142 a 3 95x1020 J and 2 4kW m 2 b 3 95x1026 J and 1 8kW m c 3 95x1022 J and 1 4kW m 2 d 3 95x1026 J and 1 4kW m 2

61 A wire of length 1 m and radius 1 mm is heated via an electric current to pro duce 1 kW of radiant power Treating the wire as a perfect blackbody and ignoring any end effects calculate the temperature of the wire

A horizontal pipe 6 m long and 12 5 cm in diameter is maintained at a temperature of 150 C in a large room where the air is 20 C and 1 atm The walls of the room are at 38 C Assume that 0 7 for the pipe How much heat is lost by the pipe through both convection and radiation

A closed cubical box made of perfectly insulating material has walls of thickness 8 cm and the only way for heat to enter or leave the box is through two solid metal plugs A and B each of cross sectional area 12 cm and length 8 cm fixed in the opposite walls of the box as shown in the figure Outer surface A is kept at 100 C while the outer surface A is kept at 4 C The thermal conductivity of the material of the plugs is 0 5 cals cm C A source of energy generating 36 cals 1 is enclosed inside the box The equilibrium temperature of the inner surface of the box assuming that it is same at all points on the inner surface is 100 C A B 4 C

A cooling curve is plotted between the temperature of a hot body and time Which of the following is not true for the cooling curve 1 Cooling is faster from a calorimeter having a larger surface area than a smaller one 2 Cooling is faster from a calorimeter painted black from outside than that from a polished surfaced calorimeter 3 Cooling is faster from a copper calorimeter than from a steel calorimeter 4 The rate of cooling remains same throughout the experiment Hence the graph is a straight line The escape velocity of a body on the surface of the earth is 11 2 kms If the earth s mass

B The time taken by ice on the surface of a pond grow from zero initial thickness to a thickness 2 5 cm is 25 hrs Find the time taken to grow fr 1 5 cm to 2 cm 1 9 hrs 3 5 hrs 2 6 hrs 4 7 hrs

A chunk of metal with a mass of 0 800 kg and 1 500 kg of water are separated from each other and are at different temperatures The metal is then immersed in the water and the combined system is thermally isolated from the environment After the metal was dropped in the water the temperature of the water increased by 3 00 C while the temperature of the metal decreases by 40 00 C The specific heat capacity of water is 4184 J kg K 1 What is the specific heat capacity of the metal 279 J kg K 1 O 314 J kg K 1 465 J kg K 1 471 J kg 1 K 1 167 J kg 1 K 1 588 J kg 1 K 1

objects are placed in a room with perfectly absorbing walls maintained at a temperature T TA T TB The objects A and B attain the temperature T eventually Select the correct statements from the following A A only emits radiation while B only absorbs it until both attain the temperature T Sec Sr Super60 All Space for rough work Page 4 Sri Chaitanya IIT Academy 06 06 2021 Sr Super60 All Jee Adv 2018 P2 GTA 08 Q P B A loses more heat by radiation than it absorbs while B absorbs more radiation than it emits until they attain the temperature T

A steel ball of mass m 1 kg 1 moving with velocity 50 m s collides S with another ball of mass m 200 g m2 lying on the ground Due to collision the KE is lost and their internal energies change equally and T and T2 are the temperature changes of masses m and m2 respectively If the specific heat of steel is unity and J 4 18 J cal 1 then

area A rod of length 5 m is prevented thermal expansion by fixing its ends rigidly is 40 cm Its cross sectional Calculate thermal stress developed on a temperature rise of 20 C if Y 2 1011 Nm 2 and a 1 2 x 10 5 K 1 NCERT Pg 283 1 2 4 x 103 N m 2 2 4 x 107 N m X 3 4 8 x 107 N m 4 5 6 107 N m

4 A room at 20 C is heated by a heater of power 2 kW The temperature is uniform throughout the room and the heat is transmitted thrugh a glass window of area 1 m and thickness 0 2 cm Calculate the temperature outside Thermal conductivity of glass is 0 2cal m C sec and mechanical equivalent of heat is 4 2 J cal a 15 24 C b 15 22 C c 15 23 C d 15 26 C

Q 45 A cylindrical rod of length 1 thermal conductivity k and area of cross section A has one end in a furnace maintained at constant temperature The other end of the rod is exposed to surrounding The curved surface of the rod is well insulated from the surrounding The surrounding temperature is To and the furnace is maintained at T To AT The exposed end of the rod is found to be slightly warmer then the surrounding with its temperature maintained T To AT AT To The exposed surface of the rod has emissivity e Prove that AT is proportional to AT2 and find the proportionality constant 1 2 2 T Furnace Rod A Insulation T To

A hollow cylinder made of thermally insulating material is equipped with a horizontal piston P of mass m and area A The piston is also made by thermally insulating material There is no friction between inner surface of the cylinder and the piston Above the piston a liquid of density p is filled up to the brim of the cylinder The piston supported at the position shown due to pressure of an ideal gas filled in the bwer portion of the cylinder When the gas is heated by the heater H it expands and pushes the piston up spilling the water out of the cylinder Number of moles of the gas is n atmospheric pressure is po and initial temperature is To A Work done by gas is pohA 0 5pgh2 A mgh B Work done by gas is 0 5 pohA pgh A meh C Final temperature of the gas is 2T D Final temperature of the gas is 2T PO A PoA pghA mg Po A mg ROA pehA me P H 0000

SolveLancer Test The appearance of colour of hot objects is as per Kirchhoff s law of radiation It means a hot object will emit only that colour which it absorbed during heating Now consider the following statements i When a red object is heated to red hot it will not be able to absorb red colour hence in darkness it will become invisible ii When a red object is heated to white hot it will absorb all colours except red and hence its colour will be cyan iii When a blue glass is heated to red hot as per Kirchhoff s law will reflect red and will appear blue iv When blue glass is heated to white hot it will absorb all colours except blue and hence its colour will be yellow SolveLancer Test a Only i correct b Both ii iii incorrect c Only iii correct d i ii iv correct

A refrigerator has to transfer an average of 26 J of heat per second from temperature 10 C 27 C Assuming no other power losses th average power consumed by the refrigerator watt is 1 300 3 187 2 263 4 37

Two rods of copper and brass having the same length and cross section are joined end to end The free end of the copper rod is at 0 C and of the brass rod is at 100 C in steady state If thermal conductivity of copper is 4 times of that of brass find the temperature at the junction of two rods Question Type Single Correct Type 1 80 C 2 60 C 3 40 C

57 The ends of a copper rod of length 1m and area of cross section 1 cm are maintained at 0 C and 100 C At the centre power is supplied at a constant rate of 25 J s The temperature gradient on higher temperature side of the rod in steady state will be K 400 J m K s lo viivito a 150 50 C m c 212 5 C m b 325 75 C m d 126 25 C m 0

Two similar rods but of different materials are joined together end to end The ratio of their thermal conductivities is 2 3 The composite rod is lagged between meting ice at 0 C and steam at normal pressure with steam on side of metal with lower value of conductivity The temperature of the junction will be O 60 C O 50 C O 40 C O 30 C

on 14 A sphere of radius R is at an absolute temperature T The missivity of the surface depends on the angles e measured from a reference e sin 0 If the total radiant ne passing through the center of the sphere as ower emitted by the sphere is NR aT where is stefan s constant then fin he integer nearest to N

Question 12 A system of rods is assembled such that each rod has a length f and cross sectional area S The mode of heat transfer is conduction and the system is in steady state The temperature of junction A is T and that of C is 2T Thermal conductivities of rods are mentioned in term of k Now answer the following questions D A 2k k k k 2k C B Temperature of junction B is Options a 1 4T b 1 6T c 1 8T

dry air was bubbled through a bulb containing 26 66 g of an organic compound in 200 g of water then through a bulb at the same temperature containing water and finally through a tube containing anhydrous calcium chloride The loss of mass in the bulb containing water was 0 087 g and the gain in the mass of the calcium chloride tube was 2 036 g Calculate the molecular mass of the organic substance Sol Po Ps Po 0 087 2 036 Loss in mass of solvent bulb Gain in mass of CaCl tube 0 087 2 036 Let the molecular mass of the organic substance be Mw2 According to Raoult s law Po Ps p W Mw 2 W2 W Mw Mw 26 66 Mw 26 66 200 Mwa 18 what about this mw 26 66 200 26 66 Mw 18

During a dry period in Earth s history riverine fluxes to the oceans were only 5 x 10 km yr What was the residence of water in the oceans during this period What was annual precipitation Assume steady state and show all work

Three rods made of same material having the same cross section have been joined as shown in the figure Each rod is of the same length The left and right ends are kept at 0 C 90 C respectively The temperature of the junction of the three rods will be A 45 C C 30 C OFC 90 C 90 C B GO C D 20 C

at 35 One end of a conducting rod is maintained temperature 50 Cand at the other end ice is melting at 0 C The rate of melting of ice is doubled if a the temperature is made 200 C and the area of cross section of the rod is doubled b the temperature is made 100 C and length of the rod is made four times c area of cross section of rod is halved and length is doubled d the temperature is made 100 C and area of cross section of rod and length both are doubled

5 A ring consisting of two parts ADB and ACB of same conductivity K carries an amount of heat H The ADB part is now replaced with another metal keeping the temperatures T and T2 constant The heat carried increases to 2H What should be the conductivity of the new ADB part Given ACB ADB 3 a 73512 K c K T C D B T2 b 2K d 3K 24

Three rods of equal length area of cross section and thermal conductivity are connected as shown in the figure There is no heat loss through lateral surface of the rods and temperature of 100 C TB 70 C and ends are TA Tc 50 C Find the temperature of junction A J B

ion Three rods of material x and three of material y are connected as shown in figure All the rods an dentical in length and cross sectional area If the end A is maintained at 60 C and the junction ut 10 C calculate the temperature of the junction B The thermal conductivity of x is 800 Wir C and that of y is 400W m C 60PC goow n goow wfC 40

Consider two hot bodies B and B2 which have temperatures 100 C and 80 C respectively at t 0 The temperature of the surroundings is 40 C The ratio of the respective rates of cooling R and R of these two bodies at t 0 will be R R 3 2 R R 5 4 R R 2 3 R R 4 5

A metal ball of surface area 200 cm and temperature 527 C is surrounded by a vessel at 27 C If the emissivity of the metal is 0 4 then the rate of loss of heat from the ball is o 5 67 108J m s k 108 joules approx 168 joules approx 182 joules approx

A layer of ice 0 C of the thickness x is floating on a pond of water L p and k respectively are the latent heat of fusion of water density of ice and thermal conductivit of ice If the atmospheric temperature is T C the time taken for the thickness of the layer of ice to increase from x to X is given by PL 2kT x1 x PL RF x2 KT 27 x x pL x x

Thermal Properties of Matter Heat and Temperature 24 A copper block of mass 2 5 kg is heated in a furnace to a temperature of 500 C and then placed on a large ice block What is the maximum amount of ice that can melt Specific heat of copper 0 39 J g 1 C 1 Latent heat of fusion of ice 335 J g Ans 1 455 kg 25 When 0 2 kg of brass at 100 C is dropped into 0 5 kg of water at 20 C The resulting temperature of water VII 939 is 23 C Calculate the specific heat of brass Specific heat of water 4 2 x10 J kg C 1 Ans 409 09 J kg C 1 26 75 g of water at 100 C is added to 20 g of ice at 15 C Determine the resulting temperature Given that latent heat of ice 80 cal g1 and specific heat of ice Ans 60 5 C 0 5 cal g 1 C 1

The temperature of an air stream flowing with a velocity of 3 m s is measured by a copper constantan thermocouple which may be approximated as sphere of 3 mm in diameter Initially the junction and air are at a temperature of 25 C The air temperature suddenly changes to and is maintained at 200 C Take p 8685 kg m Cp 383J kg K and k 29 W m K and h 150 W m K Determine i Thermal time constant and temperature indicated by the thermocouple at that instant ii Time required for the thermocouple to indicate a temperature of 199 C iii Discuss the suitability of this thermocouple to measure unsteady state temperature of fluid then the temperature variation in the fluid has a time period of 30 seconds

Suppose that in winter the daytime temperature in a certain office building is maintained at 70 F The heating is shut off at 10 P M and turned on again at 6 A M On a certain day the temperature inside the building at 2 A M was found to be 65 F The outside temperature was 50 F at 10 P M and had dropped to 40F by 6 A M What was the temperature inside the building when the heat was turned on at 6 A M Physical information Experiments show that the time rate of change of the temperature 7 of a body B which conducts heat well for example as a copper ball does is proportional to the difference between T and the

Tor Two identical bodies are made of a material which the heat capacity increases with temperature One of these is at 100 C while the other one is at 0 C If the two bodies are brought into contact then assuming no heat loss the final common temperature is 1 less than 50 C but greater than 0 C 2 0 3 50 C 4 more than 50 C

15 A block of ice at 10 C is slowly heated and converted to steam at 100 C Which of the following curves represents the phenomena qualitatively 2000 2M a c Temperature Temperature Heat supplied Heat supplied b d Temperature Temperature Heat supplied Heat supplied

A gas turbine blade made of stainless steel k 32 W m deg is 70 mm long 500 mm cross sectional area and 120 mm perimeter The temperature of the root of blade is 500 C and it is exposed to the combustion product of the fuel passing from turbine at 830 C If the film coefficient between the blade and the combustion gases is 300 W m deg determine i The temperature at the middle of blade ii The rate of heat flow from the blade

3 A thermal conductor of uniform cross sectional area A has its thermal conductivity decreasing from end A towards end B with end A maintained at higher temperature T A T T T T T T If steady state has been achieved identify the correct option 1 temperature of mid point B 2 temperature of mid point T T 2 T T 2 3 heat current amount of heat energy flowing per second is more in the left half 4 both 2 and 3