Question

An ice-box is made of wood 1.75 cm thick, lined inside with cork 2 cm thick. If the temperature of the inner surface of the cork is steady at 0oC and that of the outer surface is steady at 12oC, what is the temperature of the surface? The thermal conductivity of wood is 5 times that of cork.

                                                         

Solution

Correct option is

10.2oC

 

Let be the temperature of the interface in the steady state. Since the rate of flow of heat through wood and cork must be the same in the steady state, we have

            

Where S is the area of the interface. Thus we have

                      

Or                  

Which gives           T = 10.2oC

SIMILAR QUESTIONS

Q1

The dimensions of the coefficient of thermal conductivity are

Q2

Two different metal rods of the same length have their ends kept at the same temperatures and  with . If A and are their cross-sectional areas and k1 and k2 their thermal conductivities, the rate of flow of heat in the two rods will be the same if

Q3

Two rods A and B of different materials are welded together as shown in Fig. If their thermal conductivities are k1 and k2 , the thermal conductivity of the composite rod will be

                                                        

Q4

A one liter flask contains some mercury. It is found that at different temperatures the volume of air inside the flask remains the same. What is the volume of mercury in the flask? Given the coefficient of linear expansion of glass  oC–1, the coefficient of volume expansion of mercury is  oC–1.

Q5

A wire of cross-sectional area A at temperature t is held taut with negligible tension between two rigid supports. If the wire is cooled to a temperature  what tension is developed in the wire? The coefficient of linear expansion is  and the Young’s modulus of the wire is Y.

Q6

Two uniform brass rods A and of length l and 2and radii 2r and rrespectively are heated to the same temperature. The ratio of the increase in the length of A to that of B is

Q7

Two rods of different materials having coefficients of thermal expansion  and Young’s modulii Y1Y2 respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of the rods. If  the thermal stresses developed in the two rods are equal provided Y1 : Y2 is equal to:

Q8

The water equivalent of a copper calorimeter is 4.5 g. If the specific heat of copper is 0.09 cal.g–1oC–1 the

Q9

A slab of stone of area 0.34 m2 and thickness 10 cm is exposed on the lower face to steam at 100oC. A block of ice at 0oC rests on the upper face of the slab. In one hour, 3.6 kg of ice is melted. Assume that the heat loss from the sides is negligible. The latent heat of fusion of ice is  What is the thermal conductivity of the stone in units of Js–1m–1oC–1?

Q10

The tungsten filament of an electric lamp has a surface area A and a power rating P. if the emissivity of the filament is  is Stefan’s constant, the steady temperature of the filament will be