Conductivity is the property of a material to allow the flow of heat or electricity through it. Thermal conductivity measures heat transfer, while electrical conductivity measures electric current flow. Good conductors like metals have high conductivity, enabling efficient transfer, while insulators like wood have low conductivity and restrict energy flow.
Chapter 10 Thermal Properties of Matter focuses on heat transfer and thermal expansion. It covers concepts like specific heat capacity thermal conductivity and expansion of solids liquids and gases. Understanding these properties is crucial for applications in daily life and industries. It explains conduction convection and radiation as heat transfer modes.
Heat Current (Q):
Heat current refers to the rate at which heat energy flows through a material. It depends on the temperature difference across the material, its area, the length of the material, and its thermal conductivity.
Mathematical Expression for Heat Current:
The heat current Q is given by Fourier’s Law of Heat Conduction:
Q = (K A (T1 – T2)) / L
Where:
– Q = Heat current (rate of heat flow) in watts (W)
– K = Thermal conductivity of the material (W/m·K)
– A = Cross-sectional area through which heat flows (m²)
– T1 – T2 = Temperature difference between the two ends of the material (K or °C)
– L = Length of the material through which heat flows (m)
Thermal Resistance (R):
Thermal resistance is a measure of a material’s resistance to the flow of heat. It depends on the material’s thermal conductivity, length, and area.
Mathematical Expression for Thermal Resistance:
The thermal resistance R is given by:
R = L / (K A)
Where:
– R = Thermal resistance (K·m²/W)
– L = Length of the material (m)
– K = Thermal conductivity of the material (W/m·K)
– A = Cross-sectional area (m²)
Relationship Between Heat Current and Thermal Resistance:
Using the expression for thermal resistance, the heat current can also be written as:
Q = (T1 – T2) / R
Where R is the thermal resistance of the material. This shows that heat current is directly proportional to the temperature difference and inversely proportional to the thermal resistance.
Summary:
– Heat current is the rate of heat transfer through a material, given by Q = (K A (T1 – T2)) / L.
– Thermal resistance is the resistance to heat flow, given by R = L / (K A).
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