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****.**