procedure for determining the thermal conductivity of a solid involves embedding thermocouple in a thick slab of the material and measuring the response to a prescribed change in temperature at one surface. Consider an arrangement for which the thermocouple is embedded 10 mm from a surface that is suddenly brought to a temperature of 100degreeC by exposure to boiling water. If the initial temperature of the slab was 30degreeC and the thermocouple measures a temperature of 65degreeC, 2 minutes after the surface is brought to 100degreeC, what is the thermal conductivity. The density of the material is 2200 kg/m3 and the specific heat is 700 J/M- Find: What is the thermal conductivity of the material

The thermal conductivity  

Explanation:

From the question we are told that

  The  depth of the thermocouple from the surface is  x =  10 mm  = 0.01 m

   The  temperature is  

   The  initial temperature is  

    The  temperature of the thermocouple after t =  2 minutes( 2 * 60 =  120 \ seconds)  is  

    The  density of the material  is  

     The specific heat of the solid

Generally  the  equation for  semi -infinite medium  is mathematically as  

Here is a constant with unit

    this is from the Gaussian function table  

=>  

=>  

Generally the thermal  conductivity is mathematically represented as

molecules are free to separate from each other and will take on the shape of the container. molecules move completely at random and high speeds. they vibrate in a fixed position and do not move around much. molecules expand to the edge of their container.