How to Calculate and Solve for Thermal Conductivity of Gases | Energy Transport

The image above represents thermal conductivity of gases. To calculate thermal conductivity of gases, four essential parameters are needed and these parameters are Viscosity (η), Heat Capacity at Constant Pressure (c_p), Gas Constant (R) and Molar Mass of Gas (M).

The formula for calculating thermal conductivity of gases:

k = η(c_p + ^1.25R/_M)

Where:

k = Thermal Conductivity of Gases
η = Viscosity
c_p = Heat Capacity at Constant Pressure
R = Gas Constant
M = Molar Mass of Gas

Let’s solve an example;
Find the thermal conductivity of gases when the viscosity is 12, the heat capacity at constant pressure is 18, the gas constant is 22 and the molar mass of gas is 14.

This implies that;

η = Viscosity = 12
c_p = Heat Capacity at Constant Pressure = 18
R = Gas Constant = 22
M = Molar Mass of Gas = 14

k = η(c_p + ^1.25R/_M)
That is, k = 12(18 + ^1.25(22)/₁₄)
k = 12(18 + ^27.5/₁₄)
k = 12(18 + 1.96)
So, k = 12(19.96)
k = 239.57

Therefore, the thermal conductivity of gases is 239.57 W/mK.

Calculating the Viscosity when the Thermal Conductivity of Gases, the Heat Capacity at Constant Pressure, the Gas Constant and the Molar Mass of Gas are Given

η = ^k / _{(cp + ^1.25R / M)}

Where:

η = Viscosity
k = Thermal Conductivity of Gases
c_p = Heat Capacity at Constant Pressure
R = Gas Constant
M = Molar Mass of Gas

Let’s solve an example;
Find the viscosity when the thermal conductivity of gases is 40, the heat capacity at constant pressure is 22, the gas constant is 2 and the molar mass of gas is 8.

This implies that;

k = Thermal Conductivity of Gases = 40
c_p = Heat Capacity at Constant Pressure = 22
R = Gas Constant = 2
M = Molar Mass of Gas = 8

η = ^k / _{(cp + ^1.25R / M)}
η = ⁴⁰ / _{(22 + ^1.25(2) / 8)}
So, η = ⁴⁰ / _{(22 + ^2.5 / 8)}
η = ⁴⁰ / _{(22 + 0.313)}
That is, η = ⁴⁰ / _22.313
η = 1.79

Therefore, the viscosity is 1.79.

Read more: How to Calculate and Solve for Thermal Conductivity | Heat Capacity per Unit Volume | Energy Transport

Calculating the Heat Capacity at Constant Pressure when the Thermal Conductivity of Gases, the Viscosity, the Gas Constant and the Molar Mass of Gas are Given

c_p = kη – (^1.25R / _M)

Where:

c_p = Heat Capacity at Constant Pressure
k = Thermal Conductivity of Gases
η = Viscosity
R = Gas Constant
M = Molar Mass of Gas

Let’s solve an example;
Find the heat capacity at constant pressure when the thermal conductivity of gases is 20, the viscosity is 5, the gas constant is 4 and the molar mass of gas is 10.

This implies that;

k = Thermal Conductivity of Gases = 20
η = Viscosity = 5
R = Gas Constant = 4
M = Molar Mass of Gas = 10

c_p = kη – (^1.25R / _M)
c_p = (20)(5) – (^1.25(4) / ₁₀)
So, c_p = 100 – (⁵ / ₁₀)
c_p = 100 – 0.5
c_p = 99.5

Therefore, the heat capacity at constant pressure is 99.5

Calculating the Gas Constant when the Thermal Conductivity of Gases, the Viscosity, the Heat Capacity at Constant Pressure and the Molar Mass of Gas are Given

R = ^{(kη – c_p)M} / _1.25

Where:

R = Gas Constant
k = Thermal Conductivity of Gases
η = Viscosity
c_p = Heat Capacity at Constant Pressure
M = Molar Mass of Gas

Let’s solve an example;
Find the gas constant when the thermal conductivity of gases is 14, the viscosity is 2, the heat capacity at constant pressure is 8 and the molar mass of gas is 12.

This implies that;

k = Thermal Conductivity of Gases = 14
η = Viscosity = 2
c_p = Heat Capacity at Constant Pressure = 8
M = Molar Mass of Gas = 12

R = ^{(kη – c_p)M} / _1.25
That is, R = ^{(14(2) – 8)12} / _1.25
R = ^{(28 – 8)12} / _1.25
R = ⁽²⁰⁾¹² / _1.25
So, R = ²⁴⁰ / _1.25
R = 192

Therefore, the gas constant is 192.

Read more: How to Calculate and Solve for Total Conductivity | Thermal Properties

Calculating the Molar Mass of Gas when the Thermal Conductivity of Gases, the Viscosity, the Heat Capacity at Constant Pressure and the Gas Constant are Given

M = ^1.25R / _{(kη – cp)}

Where:

M = Molar Mass of Gas
k = Thermal Conductivity of Gases
η = Viscosity
c_p = Heat Capacity at Constant Pressure
R = Gas Constant

Let’s solve an example;
Find the molar mass of gas when the thermal conductivity of gases is 4, the viscosity is 6, the heat capacity at constant pressure is 3 and the gas constant is 9.

This implies that;

k = Thermal Conductivity of Gases = 4
η = Viscosity = 6
c_p = Heat Capacity at Constant Pressure = 3
R = Gas Constant = 9

M = ^1.25R / _{(kη – cp)}
M = ^1.25(9) / _{(4(6) – 3)}
So, M = ^11.25 / _{(24 – 3)}
M = ^11.25 / ₂₁
M = 0.53

Therefore, the molar mass of gas is 0.53.

How to Calculate Thermal Conductivity of Gases Using Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the thermal conductivity of gases.

Now, Click on Energy Transport under Materials and Metallurgical

Now, Click on Thermal Conductivity of Gases under Energy Transport

The screenshot below displays the page or activity to enter your values, to get the answer for the thermal conductivity of gases according to the respective parameter which is the Viscosity (η), Heat Capacity at Constant Pressure (c_p), Gas Constant (R) and Molar Mass of Gas (M).

Now, enter the values appropriately and accordingly for the parameters as required by the Viscosity (η) is 12, Heat Capacity at Constant Pressure (c_p) is 18, Gas Constant (R) is 22 and Molar Mass of Gas (M) is 14.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the thermal conductivity of gases and presents the formula, workings and steps too.