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Thermal conductivity is the ability of any material to conduct or transfer heat. It is generally denoted by the letter ‘k’. Heat transfer rate is lower in materials having lower thermal conductivity than in materials having higher thermal conductivity.
- Metals have high thermal conductivity and are very efficient at conducting heat while insulating materials like Rockwool or Styrofoam have thermal conductivity.
- High thermal conductivity materials are used in heat sink applications, and low conductivity materials are used as thermal insulation.
- It can also be defined as the amount of heat per unit time per unit area that can be conducted through a plate of unit thickness of a given material, the faces of the plate differing by one unit of temperature.
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Key Terms: Heat Transfer, Conductivity, Heat Flux, Temperature, SI units, Temperature gradient, Lee’s disc method, Metals, Non-metals
What is Thermal Conductivity?
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The intrinsic property of any given material to conduct and transfer heat is called thermal conductivity. This process is one of the three methods of heat transfer, the other two being convection and radiation.
- The rate at which heat is transferred is slower in materials of low thermal conductivity like Styrofoam, while it is higher in materials with high thermal conductivity like metals.
- In terms of appropriate rate equations, the heat transfer processes can be quantified.
- The reciprocal of thermal conductivity is known as thermal resistivity.
- In heat sinks, usually, materials with high thermal conductivity are used whereas materials with low thermal conductivity are used as thermal insulators.
The rate equation in this model is based on Fourier’s law of thermal conduction (also known as the law of heat conduction). The law states that the rate at which heat is transferred through a material is proportional to the negative of the temperature gradient and is also proportional to the area through which the heat flows. Through the following equation, the differential form of this law can be expressed.
q = -k.∇T
Where
- q → Heat flux or thermal flux (W.m-²)
- k → Thermal conductivity (W.m-¹.K-¹)
- ∇T → Temperature gradient (K.m-¹)
It is also the defining law of thermal conductivity.
Each substance has its own capacity to conduct heat and the thermal conductivity of that material is described by the following formula.
K = (Qd) / (AΔT)
Where
- K → thermal conductivity (W/m.K)
- Q → amount of heat transferred through the material (Joules/second or Watts)
- d → distance between the two isothermal planes
- A → area of the surface in (sq.m)
- ΔT → difference in temperature (Kelvin)
Unit Of Thermal Conductivity
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Thermal Conductivity is measured in different units across different systems. The most commonly used system of units is the SI unit system.
- SI Unit System: Thermal conductivity is measured in terms of Watts per meter Kelvin. For smaller quantities, centimeters are also used. It can be expressed as:
W.m-¹K-¹
- Imperial System: The Imperial system measures thermal conductivity in terms of British Thermal Units (BTU), feet, and Fahrenheit. It is expressed as:
BTU.h-¹.ft-¹.°F-¹
- Dimensional Formula: The Dimension of thermal conductivity is expressed in terms of mass, length, and time.
M1L1T−3K−1
Measurement Of Thermal Conductivity
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For measuring the thermal conductivities of materials many techniques are used. These methods are broadly classified into two types of techniques: transient and steady-state techniques.
Steady-State Techniques
Where the temperature of the material in question does not change over a period of time this method is applied for measurements. The analysis is relatively straightforward since the temperature is constant and this is considered to be an advantage of this method.
- On the other hand, an important disadvantage of this technique is that they generally require a very well-engineered setup to perform the experiments.
- Searle’s bar method for measuring the thermal conductivity of a good conductor and Lee’s disc method are a few examples of the Steady-State Technique.
Transient Techniques
The measurements in this method are generally taken during the heating-up process. The measurements can be taken relatively fast and this is considered to be an advantage of this method.
- On the other hand, an important disadvantage of this technique is the difficulty in mathematically analyzing the data from the measurements.
- The transient plane source method, the transient line source method, and the laser flash method are a few examples of the Transient Technique.
Effect of Temperature on Thermal Conductivity
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The thermal conductivities of metals and non-metals are affected differently by changes in temperature.
Metals
The presence of free electrons is the main cause of the heat conductivity of metals. As per the Wiedemann-Franz law, the heat conductivity of metals is attributed to the presence of free electrons and is somewhat proportional to the product of the absolute temperature and electrical conductivity.
The electrical conductivity of a pure metal decreases if the temperature is increased.
- This means that with the increase in temperature, the thermal conductivity of the pure metal shows little variance but it decreases sharply when temperatures approach 0K.
- At temperatures ranging from 2K to 10K, it is found that heat conductivity in many pure metals reaches its peak value.
- When the temperature is increased, alloys of metals do not show significant changes in electrical conductivity i.e. with the increase in temperature their heat conductivities also increase.
Non-Metals
The presence of lattice vibrations is the main cause of the heat conductivity of non-metals. Higher temperatures do not affect the thermal conductivity of non-metals. When the temperature is decreased than the Debye Temperature, non-metals show a remarkable decrease in their heat conductivity and capacity properties.
Other Factors that Affect Thermal Conductivity
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Besides temperature, there are various other factors that too affect the thermal conductivity of a material. Some of the important factors are:
- When there is any shift in the object’s chemical phases, the heat conductivity of the concerned material may also change abruptly.
- The presence of Thermal Anisotropy in material changes the direction of the heat flow i.e. the heat will flow in the opposite direction of the temperature gradient of direction (from high to low).
- The Wiedemann-Franz law of thermal conductivity is only applicable to metals as in the case of non-metals the rate of electrical conductivity does not affect their heat conductivity.
- The Maggi-Righi-Leduc effect describes the effect a magnetic field has on the thermal conductivity of a material. It is observed that an orthogonal temperature gradient is formed when a magnetic field is introduced in the process.
- The isotopic purity of the crystal also affects the heat conductivity of a material. The higher the purity of a substance, the higher the thermal conductivity and capacity.
Uses Of Thermal Conductivity
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The uses od thermal conductivity are:
- Metals with good thermal conductivity are used in hot water tanks, underfloor heating systems, refrigeration, etc.
- It is also widely used in electricals and electronics such as disk drives, Computers, and TV sets.
- Metals with good thermal properties are an ideal choice for kitchen vessels and utensils.
- Substances with low conductivity are used as insulators.
Things To Remember
- Thermal conductivity is the ability of any material to conduct or transfer heat.
- Thermal Conductivity is expressed by q = -k.∇T
- The SI unit of Thermal Conductivity is W.m-¹K-¹
- The imperial unit of Thermal Conductivity is BTU.h-¹.ft-¹.°F-¹
- The Dimensional unit of thermal conductivity is M1L1T−3K−1
- The thermal conductivity of a pure metal decreases if the temperature is increased.
- Substances with low conductivity are used as insulators.
Sample Questions
Ques. Which metal is the best conductor of heat? (2 marks)
Ans. All metals like brass, iron, steel, gold, and mercury are basically good conductors of heat. However, copper is the best metal and hence is used in the overhead electric lines that supply electricity to trains.
Ques. Why does heat flow from one object to another through conduction? (2 marks)
Ans. Typically conduction happens in solids and it happens due to the difference in temperature i.e. the temperature gradient. In this process, only the heat energy is passed from the hotter side to the colder side without the movement of molecules.
Ques. What material is used to line the bottom of a stainless steel pan? (2 marks)
Ans. The stainless steel pans often have a copper bottom for faster cooking as copper is a better conductor of heat than steel.
Ques. Why do railway lines have gaps between them? (2 marks)
Ans. Railway tracks have gaps provided between the rails. Since the rails are made of iron which is a good conductor of heat, the gaps are given for them to expand and contract during the summer and winter seasons due to the change in temperatures.
Ques. What happens if a metal heated to 45 C is dropped in the water at 45 C? (2 marks)
Ans. We all know that heat transfers from the higher point to the lower point. Despite the substances being different in nature since both of them have the same temperature, no heat transfer will take place between the metal and water.
Ques. What are the different methods of Heat Transfer? (5 marks)
Ans. Heat can be transferred from one place to another by three different methods, namely, conduction, convection, and radiation. Conduction usually takes place in solids, convection in liquids and gases, and no medium is required for radiation.
(i) Conduction: According to Maxwell, conduction is the flow of heat through an unequally heated body from places of higher temperature to those of lower temperature. The rate of heat transfer is given by
where K is called Thermal Conductivity and A is the area of cross-section.
(ii) Convection: Maxwell defines convection as the flow of heat by the motion of the hot body itself carrying its heat with it.
(iii) Radiation: Radiation is the mode of heat transfer in which heat travels directly from one place to another without the agency of any intervening medium.
Thermal conductivity is defined as heat energy transferred in unit time from the unit area having a unit difference in temperature over a unit length. It is expressed in Js-1 m-1 °C-1 or W-1 K-1
Ques. Heat is associated with Kinetic energy. Explain. (2 marks)
Ans. When a body is heated its temperature rises and in liquids and gases, the vibration of molecules about their mean position increases, hence kinetic energy associated with the random motion of molecules increases.
So, thermal energy or heat is associated with the random and translatory motions of molecules.
Ques. Define Thermal Stress. (3 marks)
Ans. When a rod is held between two fixed supports and its temperature is increased, the fixed supports do not allow the rod to expand, which results in stress which is called thermal stress.
Thermal stress in the rod is given by
where Y is Young’s modulus for the material of the rod, A is the area cross-section of the rod, A is the coefficient of linear expansion and F is the developed force in the rod.
Ques. What is Thermal Expansion? (2 marks)
Ans. The increase in the size of a body due to the increase in temperature is called thermal expansion. Three types of expansions can take place in solids viz. linear, superficial, and volume expansion.
Ques. Why is copper said to have a high thermal conductivity? (2 marks)
Ans. Copper is said to have a high thermal conductivity because copper is a lattice of positive copper ions. It has free electrons that move between them. These free electrons help in electrical conduction.
Ques. Define Thermal Capacity. (2 marks)
Ans. The thermal capacity of a body is the quantity of heat required to raise the temperature of the whole of the body through a unit degree. It is measured in calories per °C or joule per K.
If Q is the amount of heat needed to produce a change in temperature (Δt) of the substance, then the thermal capacity of the substance is given by
The dimensional formula of heat capacity is [ML2T -2K-1 ]
Ques. Define Specific Heat Capacity. (2 marks)
Ans. The specific heat capacity (also referred to as specific heat) of a substance is the amount of heat required to raise the temperature of a unit mass of substance through 1 °C. It is measured in cal g-1(°C)-1 or J kg-1 K-1.
The specific heat capacity of a substance is given by
where m is the mass of the substance and Q is the heat required to change its temperature Δt.
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