Thermal Conductivity

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In physics, thermal conductivity, k, is the intensive property of a material that indicates its ability to conduct heat. It is defined as the quantity of heat, Q, transmitted in time t through a thickness L, in a direction normal to a surface of area A, due to a temperature difference ΔT, under steady state conditions and when the heat transfer is dependent only on the temperature gradient.

thermal conductivity = heat flow rate × distance / (area × temperature difference)

Try the following problems, using the above equation.  

The drawing shows a composite slab consisting of three materials through which heat is conducted from left to right. The materials have identical thicknesses and cross-sectional areas. Rank the materials according to their thermal conductivities, largest first.

Composite slab Image is teacher-created

  • (Answer: k3, k2, k1)

Heat is conducted through the two slabs shown in the drawing. The slabs have identical thicknesses and cross-sectional areas, but they are made from different materials. The thermal conductivity of slab 1 is k 1 = 85 J/(s · m · C ° ). What is the thermal conductivity k 2 of slab 2? Give your answer to two significant figures, e.g., 45 J/(s · m · C °).

slab thermal conductivity Image is teacher-created

  • (Answer: 170smC)

A can of gasoline has a rectangular base with dimensions of 13.5 cm by 13 cm. If there are 3 liters of gasoline in the can, how much does the surface of the gasoline rise (in mm) in the can when the temperature is raised by 45oC? The coefficient for volume expansion of gasoline is 9.5 x 10-4/oC.

  • (Answer: 7.29mm)

 

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