**Heat Transfer**

- This video introduces the different methods of heat transfer like conduction and convection which requires a medium and radiation which does not require a medium.
- This video discusses the process conduction in detail. It also explains the different states of conduction and the rate of heat flow depending upon the coefficient of conductivity or conductance of the medium.
- A slab of unknown material of given area and thickness is exposed on the lower surface to steam at 100 0C. A block of ice at 0 0C rests on the upper surface of the slab. If in one hour, 10 kg of ice is melted, calculate the thermal conductivity of the material; given the latent heat.
- This video explains the heat transfer by conduction in a situation in which two slabs of equal area and thickness but different conductivity, arranged in series and parallel is used as a medium. It also explains the method to derive the effective conductivity of the slabs.
- A composite sheet has two layers A and B each made of different material. Both layers have the same thickness. The thermal conductivity of A is 3 times as that of B. In the steady state, the temperature difference across the composite sheet is 36 0C. Find the temperature difference (in 0C) across the layer A.
- In one case, two identical rods are joined one after the other and the temperature at one of the ends of this combination is maintained at 100 0C and the other is kept in ice at 0 0C. In the second case, the two rods are placed one on top of the other and has the same temperature difference across its ends. If Q1 and Q2 (in gram per second) are the respective rates of melting of ice in the two cases, then their ratio Q1/Q2 is.....?
- A cylinder of radius R and thermal conductivity k1, is surrounded by a cylindrical shell of inner radius R and outer radius 2R and of thermal conductivity k2. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system will be ....?
- A room of a given total wall area is heated by an electric heater to maintain a temperature of 30 0C inside it when the outside temperature is -10 0C. The walls have three layers of materials having different thermal conductivities and different thickness. Find the power of the electric heater and the temperature at every interface. Assume that there is no heat loss through the floor and ceiling.
- Three rods of identical cross-sectional area and made from the same metal form the sides of an isosceles triangle ABC, right angled at C, . The point A and C are maintained at temperatures T and √2 T respectively. If temperature of point B is TB, the ratio TB / T is .....?
- This video explains the process of heat transfer by conduction through layer of a cylindrical shells and the method to derive effective conductivity of shell.
- A thin metal pipe of given length and radius carries steam at 100 0C. This is covered by two layers of insulation with known thermal conductivities. If the outer surface of lagging is kept in ice at 0 0C, find the following. (a) the temperature of cylindrical interface of insulating materials (b) the mass of steam condensed per second (c) mass of ice melting per second.
- This video discusses the Stefan's law which governs the process of heat transfer by radiation from a source like a hot body. It also explains the different characteristics on which the rate of heat transfer by radiation depends like emissivity, and absorptivity of the body, along with Prevost theory of exchange.
- A thin rectangular sheet of given side lengths is heated in a furnace to 800 K and taken out. How much electric power is needed to maintain the sheet at this temperature, if the temperature of surrounding is known? Given its emissivity and stefan-Boltzmann constant.
- A copper sphere is suspended in a vacuum chamber maintained at 300 K. To maintain it at a constant temperature of 600 K by heating it electrically and then to maintain it at the temperature When surface of copper sphere is completely blackened, a known amount of power is needed. Calculate the emissivity of copper.
- This video explains a method to estimate the temperature of the sun by observing the thermal radiation received by earth from it using Stefan's law.
- This video explains the Wien's displacement law which relates the dominant radiation coming out of a black body with its absolute temperature. It also explains the range of wavelength of radiation coming out of a body at a known temperature.
- A black body is at a temperature of 2880 K. The energy of radiation emitted by this body between wavelengths 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. If the Wien's constant is given, which of the following is correct? (a) U1 = 0 (b) U3 = 0 (c) U1>U2 (d) U2 > U1
- Which of the following is the fm – T graph for a perfectly black body?
- An ideal black body at room temperature is thrown into a furnace. Which of the following is/are correct observation(s)? (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 be distinguished.
- If the filament of given power and area behaves as a perfect black body, find the wavelength and frequency corresponding to the maximum in its energy distribution. Given the Stefan's constant.
- This video illustrates a method to derive the rate of cooling of a body by Stefan's law. It also states the Newton's law of cooling which relates the law of cooling to the difference in temperature of the body and surrounding.
- A body cools down from 60 0C to 55 0C in given time and known temperature of surrounding. Calculate the following. a) the time taken by the same body to cool by another 5 0C . b) temperature of body after some time when it was at 55 0C.
- The graph shown in the figure, plot fall of temperature (T) of two bodies x and y, having the same surface area, with time (t) due to emission of radiation. Find the correct relation between emissive power (E) and absorptive power (A) between them.
- Two solid copper spheres of known radii are at a same temperature of 60 0C. If the temperature of surrounding is known, then find (a) the ratio of their initial heat loss per second from their surfaces (b) the ratio of their initial rates of cooling
- A semi-circular rod and a straight rod of the same material and of same cross-sectional area are joined as shown in the figure. The points A and B are maintained at different temperatures. The ratio of rate of heat transfer through the semi-circular rod to that of the straight rod is....?
- Inside temperature of a refrigerator of known thickness and area is maintained at different temperature than the outside constant temperature. Output power of its cooling system is equal to the rate at which heat is drained from it. If the efficiency of its cooling system is given, find the input power required to maintain the refrigerator at constant temperature. Given thermal conductivity of material of refrigerator.
- Three rods made of the same material and 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 different temperatures. The temperature of the junction of the three rods will be...?
- A double pane window is used for insulating a room thermally from outside. It consists of two glass sheets having equal area separated by air space. In the steady state, the room glass interface and the glass outdoor interface are at constant temperatures. Calculate the rate of heat flow through the window. Also find the temperature at other interfaces. Given thermal conductivities of glass and air.
- Three rods of same dimensions are arranged in a triangle as shown in the figure. They have thermal conductivities k1, k2, and k3. The points P and Q are maintained at different temperatures for the heat to flow at the same rate along PRQ and PQ. Find the relation between the thermal conductivities of rods.
- A metal rod AB of length l has its one end in ice at 0 0C and the other in water at 100 0C. If a point on the rod is maintained at a given constant temperature using a flame, then it is found that the amount of water evaporating per unit time is equal to the amount of ice melting per unit time. Find the distance of this point from ice in terms of the fraction of length of rod. Given the latent heat of vaporization of water and the latent heat of fusion of ice. Neglect any heat loss to the surrounding.
- A closed cubical box made of perfectly insulating material of known walls thickness has two solid, cylindrical, metallic plugs of which are the only ways for heat to enter or leave the box, as shown in figure. Outer surface A is kept at 100 0C while the outer surface B of the outer plug is maintained at 0 0C. A source of heat is enclosed inside the box. Find the equilibrium temperatures of the inner surface of the box assuming that it is the same at all point on the inner surface.
- Three rods AB, BC and BD having thermal conductivities in the ratio 1 : 2 : 3 and lengths in the ratios 2 : 3 : 4 are joined as shown in figure. The ends A, C and D are at known temperatures. Find the temperature of the junction B. Assume steady state.
- The intensity of radiation emitted by two stars has their maximum value at different given wavelengths. If these stars behave as black bodies, what is the ratio of their surface temperature? If the power of radiation of first star is 81 times as that of second star, the ratio of their radii will be....?
- The outer surface areas of two bodies having known thermal emissivity are the same. If they emit total radiant energy at the same rate, find the ratio of their temperatures.
- A cubical black body of side l radiates a known amount of power at T Kelvin. If the side of cube was halved and the temperature doubled, the power radiated in watt would be...?
- Earth receives 1600 Wm-2 of solar power. If all the solar energy falling on a lens of given area is focused on a block of ice of mass 5 kg, the time taken to melt the ice will be......?
- Initially a black body at absolute temperature T is kept inside a closed chamber at absolute temperature To. Now the chamber is slightly opened to allow sun rays to enter. It is observed that temperatures T and To remains constant. Which of the following statement is/are true? (a)The rate of emission of energy from the black body remains the same. (b)The rate of emission of energy from the black body increases. (c)The rate of absorption of energy by the black body increases. (d)The energy radiated by the black body equals the energy absorbed by it.
- A heat sensor of area A is at a distance d from a source at temperature T. If the temperature of source is doubled, how far the sensor should be moved from the source so that the power received by it remains the same.
- Find the relation between the temperature of a planet and its distance from the Sun. Assume both Sun and planet behave like black bodies.
- Two identical spheres A and B are suspended in an air chamber which is maintained at a temperature of 50 0C. Find the ratio of the heat lost per second from the surface of the spheres if their temperature is maintained at some different temperatures.
- A cube and a sphere of equal edge and radius, made of the same substance are allowed to cool under identical conditions. Determine which of the two will cool at a faster rate.
- Two metallic spheres S1 and S2 are made of the same material and have identical surface finish. The mass of S1 is eight times that of S2. Both the spheres are heated to the same temperature and put in the same room having lower temperature but are thermally insulated from each other. The ratio of the initial rate of cooling of S1 to that of S2 is ...?
- A solid cube of given edge length is suspended in an evacuated enclosure. Its temperature is found to fall from 100 0C to 99 0C in a given time period. Another solid cube with similar surface nature, but double the edge length is suspended in a similar manner. Find the approximate time required for this cube to cool from 100 0C to 99 0C.
- There are two thin spheres A and B of the same material and same thickness, emit like black bodies. Radius of A is double that of B and both have same temperature T. When A and B are kept in a room of temperature To ( < T ), the ratio of their rates of cooling (rates of fall of temperature) is...? (Assume negligible heat exchange between A and B)
- A sphere of radius R has its outer surface painted black. Find the time required for the sphere to cool down from T1 K to T2 K. Given the density of copper and its specific heat. Temperature of environment is negligible as compared to T1 and T2, so the rate of absorption can be neglected.
- A hot body placed in air is cooled down according to Newton's Law of cooling, the rate of decrease in temperature being B times the temperature difference with the surrounding. Find the time in which the body will lose half the maximum heat it can lose.
- A cylindrical rod of known heat capacity at temperature of 27 0C, is heated internally by heater supplying power at a given rate to raise and maintain its temperature at 77 0C. Find the following. (a) the initial rate of increase in temperature of rod (b) the rate of emission of radiant heat in steady state. If the heater is switched off, find (d) the rate of fall in temperature of the cylinder just when the heater is turned off (e) rate of fall in temperature when its temperature is 52 0C (f) the net amount of heat lost till this point (g) maximum net amount of heat lost by the cylinder.
- One end of a rod of length L cross-sectional area A is kept in a furnace at temperature T1. The other end of rod is kept at a temperature T2. The thermal conductivity of the material of the rod is k and emissivity of the rod is e. It is given that T2 = Ts + ΔT, where ΔT << Ts, Ts is the temperature of the surroundings. If ΔT is directly proportional to difference in T1 and T2, find the proportionality constant. Consider that heat is lost only by radiation at the end where the temperature of the rod is T2.
- Three rods of material x and three rods of material y are connected as shown in figure. All the rods are of identical length and cross-sectional area. If the end A is maintained at 100 0C and the junction E at 0 0C, calculate the temperature of the junctions B, C and D. The thermal conductivity of x is 3 times as that of y.
- A tapered rod of length l and thermal conductivity k has its end radii r1 and r2 maintained at temperature T1 and T2 respectively, as shown in figure. Calculate the rate of flow of heat through the rod.
- A rod of length l and cross section A is initially at room temperature. Its one end is put in furnace and the other is maintained as before. (a) Find heat absorbed by the rod before steady state is achieved. (b) If the maximum rate at which furnace can supply heat is P, find the minimum time taken to achieve steady state.
- A cylinder of given length and area of cross section is placed coaxially on a thin metal disc of given mass and of the same cross section. The upper face of the cylinder is maintained at a constant temperature of 400 K and the initial temperature of the disc is 200 K. If thermal conductivity of the material of the cylinder and the specific heat of the material of the disc is known, how long will it take for the temperature of the disc to increase to 300 K? Assume, and system to be thermally insulated except for the upper face of the cylinder.