An experimental arrangement for measuring the thermal conductivity of solid material involves the use of two very long rods that are equivalent in every aspect (dimension, shape, etc.) except that one...

An experimental arrangement for measuring the thermal conductivity of solid material involves the use of two very long rods that are equivalent in every aspect (dimension, shape, etc.) except that one is fabricated from standard material of known conductivity kA while the other is fabricated from the material whose thermal conductivity kp is desired. Both rods are attached at one end to a heat source of fixed temperature Tb , are exposed to a fluid of temperature T.. and are instrumented with thermocouple to measure the temperature at fixed distance 'x', from the heat source. If the standard material has kA = 200 W/mK and measurements reveal the value of TA= 75°C and TB= 60°C at x for Tb= 100°C and T..= 25°C, what is thermal conductivity kp of the test material?