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Important questions on Problems On Conduction

HARD

Find the temperature distribution in the space between two coaxial cylinders of radii and filled with a uniform heat conducting substance if the temperatures of the cylinders are constant and are equal to and respectively.

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HARD

According to the experiment of Ingen Hausz the relation between
the thermal conductivity of a metal rod is K and the length of the
rod whenever the wax melts 

A

B

C

D

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HARD

For bacteriological testing of water supplies and in medical clinics, samples must routinely be incubated for 24 h at . Peace Corps volunteer and MIT engineer Amy Smith invented a low-cost, low-maintenance incubator. The incubator consists of a foam-insulated box containing a waxy material that melts at interspersed among tubes, dishes, or bottles containing the test samples and growth medium (bacteria food).Outside the box, the waxy material is first melted by a stove or solar energy collector. Then the waxy material is put into the box to keep the test samples warm as the material solidifies. The heat of fusion of the phase-change material is 205 kJ/kg. Model the insulation as a panel with surface area , thickness 4.50 cm,and conductivity . Assume the exterior temperature is for 12.0 h and for 12.0 h. (a) What mass of the waxy material is required to conduct the bacteriological test? (b) Explain why your calculation can be done without knowing the mass of the test samples or of the insulation.

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HARD

A metallic rod long and  in the area is heated at one end. The coefficient of thermal conductivity of the material of the metallic rod is . In the steady-state, the temperature of the ends of the rod is and . Calculate.

  1. Temperature gradient In the rod.
  2. Temperature at a point m from the hot end.
  3. Rate of heat transmission.

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HARD

The thermal power of density is generated uniformly inside a uniform sphere of radius and heat conductivity coefficient . Find the temperature distribution in the sphere provided the steady-state temperature at its surface is equal to

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HARD

The coefficients of thermal conductivity of copper, mercury, and glass are respectively K, K, and K such that . If the same quantity of heat is to flow per second per unit area of each and corresponding temperature gradients are X, X, and X, then 

A

B

C

D

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HARD

A rod of length l with thermally insulated lateral surface consists of material whose heat conductivity coefficient varies with temperature as , where is a constant. The ends of the rod are kept at temperatures and . Find the function , where is the distance from the end whose temperature is , and the heat flow density.

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HARD

In a series of experiments, block is to be placed in a thermally insulated container with block , which has the same mass as block . In each experiment, block is initially at a certain temperature but temperature of block is changed from experiment to experiment. Let represent the final temperature of the two blocks when they reach thermal equilibrium in any of the experiments. Figure gives temperature versus the initial temperature for a range of possible values of , from to . The vertical axis scale is set by What are temperate .

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HARD

A glass windowpane in a home is 0.620 cm thick and has dimensions of 1.00 m x 2.00 m. On a certain day,the temperature of the interior surface of the glass is and the exterior surface temperature is .(a) What is the rate at which energy is transferred by heat through the glass? (b) How much energy is transferred through the window in one day, assuming the temperatures on the surfaces remain constant?

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HARD

A box with a total surface area of and a wall thickness of 4.00 cm is made of an insulating material.A 10.0-W electric heater inside the box maintains the inside temperature at above the outside temperature. Find the thermal conductivity k of the insulating material.

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