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The figure shows a system of two concentric spheres of radii r1 and r2 and kept at temperatures T1 and T2 respectively. The radial rate of flow of heat in a substance between the two concentric sphere is proportional to

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Important Questions on Heat Transfer

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JEE Main/Advance
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Three rods of the same dimensions have thermal conductivities 3k,2k and k. They are arranged as shown with their ends at 100°C, 50°C and 0°C. The temperature of their junction is:

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The area of cross-section of rod is given by A=A01+αx where A0 & α are constant and x is the distance from one end. If the thermal conductivity of the material is K, what is the thermal resistance of the rod if its length is l0?
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Radiation from a black body at the thermodynamic temperature T1 is measured by a small detector at distance d1 from it. When the temperature is increased to T2 and the distance to d2, the power received by the detector is unchanged. What is the ratio d2/d1?
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A point source of heat of power P is placed at the center of a spherical shell of mean radius R. The material of the shell has thermal conductivity k. If the temperature difference between the outer and the inner surface of the shell is not to exceed T, then the thickness of the shell should not be less than :-
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A black body emits radiation at the rate P when its temperature is T. At this temperature the wavelength at which the radiation has a maximum intensity is λ 0. If at another temperature T' the power radiated is P' and wavelength at maximum intensity is λ 0 / 2  then
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Calculate θ1 and θ2 in shown situation.

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An electric heater is used in a room of total wall area 137 m2 to maintain a temperature of +20 °C inside it, when the outside temperature is -10 °C. The walls have three different layers of materials. The innermost layer is of wood of thickness 2.5 cm, the middle layer is of cement of thickness 1.0 cm and the outermost layer is of brick of thickness 25.0 cm. The power of electric heater (in W) is x×103 W. Write the value of x to the nearest integer. Assume that there is no heat loss through the floor and the ceiling. The thermal conductivities of wood, cement and brick are 0.125, 1.5 and 1.0 W m-1 °C-1, respectively.
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JEE Main/Advance
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A double-pane window used for insulating a room thermally from outside consists of two glass sheets each of area 1 m2 and thickness  0.01 m separated by a 0.05 m thick stagnant air space. In the steady state, the room glass interface and the glass-outdoor interface are at constant temperature of 27C and 0C respectively. Calculate the rate of heat flow through the window pane. Also find the temperatures of other interfaces. Given thermal conductivities of glass and air as 0.8 and 0.08 W m-1 K-1 respectively.