Thermal Calculators

Here’s a breakdown of how to calculate each of the thermal properties you mentioned:

1. Thermal Conductivity (k)

Thermal conductivity refers to the ability of a material to conduct heat. It is a material property and depends on the type of material, temperature, and other factors.

The formula for thermal conductivity is:

Where:

• Q = Heat transfer rate (W)
• k = Thermal conductivity (W/m·K)
• A = Area of the material (m²)
• T1​ and T2​ = Temperature difference between the two sides of the material (K or °C)
• L = Thickness of the material (m)

To solve for k, rearrange the equation:

2. Thermal Resistance (R)

Thermal resistance is a measure of the ability of a material or system to resist the flow of heat. It's typically used when considering heat transfer across walls, windows, or insulation.

The formula for thermal resistance is:

Where:

• R = Thermal resistance (K/W)
• L = Thickness of the material (m)
• k = Thermal conductivity of the material (W/m·K)
• A = Cross-sectional area (m²)

3. Thermal Conductance (C)

Thermal conductance is the inverse of thermal resistance and represents the ability of a material to conduct heat.

The formula for thermal conductance is:

Where:

• C = Thermal conductance (W/K)
• k = Thermal conductivity (W/m·K)
• A = Area of the material (m²)
• L = Thickness of the material (m)

4. Specific Heat (Cp​)

Specific heat is the amount of heat required to raise the temperature of a given mass of a material by one degree Celsius (or one Kelvin).

The formula for specific heat is:

Where:

• Q = Heat energy absorbed or released (J)
• m = Mass of the substance (kg)
• Cp​ = Specific heat capacity (J/kg·K)
• ΔT = Change in temperature (K or °C)

To solve for Cp​ :

Example Calculations:

Let’s go through an example for each property:

1. Thermal Conductivity Calculation:

Given:

• Heat transfer rate Q = 100 W
• Area A = 2 m²
• Temperature difference (T1−T2) = 10°C (or 10 K)
• Thickness L = 0.5 m

So, the thermal conductivity is 2.5 W/m·K.

2. Thermal Resistance Calculation:

Given:

• L = 0.5 m
• k = 2.5 W/m·K
• A = 2 m²

So, the thermal resistance is 0.1 K/W.

3. Thermal Conductance Calculation:

Given:

• k = 2.5 W/m·K
• A = 2 m²
• L = 0.5 m

So, the thermal conductance is 10 W/K.

4. Specific Heat Calculation:

Given:

• Heat energy Q = 500 J
• Mass m = 2 kg
• Temperature change ΔT = 10°C

So, the specific heat is 25 J/kg·K.