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The relationship betweeen thermal resistivity and temperature is illustrated by the image below.

To compute for the relationship between thermal resistivity and temperature, three essential parameters are needed and these parameters are Constant of the Metal (a), Constant of the Metal (ρ_o) and Temperature (T).

The formula for calculating relationship between thermal resistivity and temperature:

ρ_t = ρ_o + aT

Where:

ρ_t = Thermal Resistivity
ρ_o = Constant of the Metal
a = Constant of the Metal
T = Temperature

Let’s solve an example;
Find the relationship between thermal resistivity and temperature when the constant of the metal is 32, the constant of the metal is 8 and the temperature is 2.

This implies that;

ρ_o = Constant of the Metal = 32
a = Constant of the Metal = 8
T = Temperature = 2

ρ_t = ρ_o + aT
ρ_t = 32 + (8)(2)
ρ_t = 32 + (16)
ρ_t = 48

Therefore, the relationship between thermal resistivity and temperature is 48 Ωm.

Calculating the Constant of the Metal when the Relationship between Thermal Resistivity and Temperature, the Constant of the Metal and the Temperature is Given.

ρ_o = ρ_t – aT

Where:

ρ_o = Constant of the Metal
ρ_t = Thermal Resistivity
a = Constant of the Metal
T = Temperature

Let’s solve an example;
Find the constant of the metal when the thermal resistivity is 32, the constant of the metal is 2 and the temperature is 4.

This implies that;

ρ_t = Thermal Resistivity = 32
a = Constant of the Metal = 2
T = Temperature = 4

ρ_o = ρ_t – aT
ρ_o = 32 – 2(4)
ρ_o = 32 – 8
ρ_o = 24

Therefore, the constant of the metal is 24.

Continue reading How to Calculate and Solve for Relationship between Thermal Resistivity and Temperature | Electrical Properties