we want to measure the thermal conductivity of an unknown insulator material. Fo

Question

we want to measure the thermal conductivity of an unknown insulator material. For this we use the following set up: A 4 mm thick plate of the unknown material is placed between two iron plates of thickness 3 cm each. All three plates are 15 cm by 15 cm in size. The upper iron plate is heated to 350 k and the lower iron plate is kept at 290 k. ONce a stationary temperature profile has developed across the insulator, the heater is removed from the upper iron plate. We observe that the temperature of upper iron plate drops by 2.5 K after 100 seconds. Neglecting any loss of heat to the environment, what is ther thermal conductivity coefficient for the unknown insulator material? Hint: density of iron is p = 7.9 g/cm3 and its specfici heat capacity is given in Table 6.4.

Explanation / Answer

ALL THREE PLATES ARE ARRANGED IN THERMAL SERIES BECAUSE THE HEAT CURRENT IS SAME IN ALL THREE PLATES THE GENERAL EXPRESSION FOR THE THERMAL RESISTANCE OF ANY PLATE IS GIVEN BY X/KA WHERE X IS THE THICKNESS OF THE SHEET K IS THE THERMAL CONDUCTIVITY AND A IS THE AREA OF CROSS SECTION when these plates are arranged in series then the equivalent thermal conductivity is given by sum for all three plates in which we dont know the thermal conductivity of insulator. dQ/dt=T-290/equivalent thermal resistance. specific heat capacity of iron*dT/dt=dQ/dt substituting s*dT/dt=T-290/equivalent thermal resistance s*dT/T-290=dt/(equivalent thermal resistance) integrate on both sides T from 350->3540-2.5 and t from 0->100sec

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