Question

A composite slap consists of two slabs A and of different materials but of the same thickness placed one on top of the other. The thermal conductivities of A and are k1 and k2 respectively. A steady temperature difference of 12oC is maintained across the composite slab. If k1 = k2/2, the temperature difference across slab A will be

Solution

Correct option is

8oC

 

Let  and  be the temperature at the two faces of the composite slab and let  be the temperature at the common face of the slab. If l is the length of each slab and A the area of their face, then, in the steady state, the rate of flow of heat across = rate of flow of heat across B, i.e.

                   

 

Now                        k2k1. Therefore

                                                          …(i)

               …(ii)

Using (ii) and (i) we have

                     

 

 

SIMILAR QUESTIONS

Q1

A thin copper wire of length L increases its length by 1% when heated from temperature T1 to T2. What is the percentage change in area when a thin copper plate having dimensions  is heated from T1 toT2?

Q2

In Fig., curves AB and CD represent the relation between pressure P and volume V of an ideal gas. One of the curves represents an isothermal expansion and the other represents an adiabatic expansion. Which curve represents an adiabatic expansion?

                                                                            

Q3

One mole of an ideal gas  at absolute temperature T1 is adiabatically compressed from an initial pressure P1 to a final pressure P2. The resulting temperatureT2 of the gas is given by

Q4

A certain mass of an ideal gas at pressure P1 is adiabatically expanded from an initial volume V1 to a final volume V2. The resulting pressure P2 of the gas is given by

Q5

A Carnot’s engine working between 27oC and 127oC takes up 800 J of heat from the reservoir in one cycle. What is the work done by the engine?

Q6

A Carnot’s engine whose sink is at a temperature of 300 K has an efficiency of 40%. By how much should the temperature of the source be increased so as to increase the efficiency to 60%?

Q7

The surface of the earth receives solar radiation at the rate of 1400 Wm – 2. The distance of the centre of the sun from the surface of the earth is  m and the radius of the sun is  m. Treating the sun as a back body, it follows from the above data that the surface temperature of the sun is about

Q8

What is the SI unit of the Boltzmann’s constant?

Q9

Two slabs and B of different materials but of the same thickness are joined as shown in Fig. 8.8. The thermal conductivities of A and B are k1and k2 respectively. The thermal conductivity of the composite slab will be

                                                                 

Q10

Two cylindrical rods of lengths l1 and l2, radii r1 and r2 have thermal conductivities k1 and k2 respectively. The ends of the rods are maintained at the same temperature difference. If l1 = 2l2 and r1 = r2/2, the rates of heat flow in them will be the same if k1/k2 is