# How to Calculate and Solve for Steady State Diffusion | Diffusion in Alloying

**Last Updated on January 12, 2023**

The image above represents steady state diffusion.

To compute for steady state diffusion, three essential parameters are needed and these parameters are **Diffusion Gradient (dC/dx), Cross-sectional Area (A) **and **Time (t).**

The formula for calculating steady state diffusion:

J = ^{dC/dx}/_{At}

Where:

J = Steady State Diffusion

dC/dx = Diffusion Gradient

A = Cross-sectional Area

t = Time

Given an example;

Find the steady state diffusion when the diffusion coefficient is 12, the cross-sectional area is 4 and time is 2.

This implies that;

dC/dx = Diffusion Gradient = 12

A = Cross-sectional Area = 4

t = Time = 2

J = ^{dC/dx}/_{At}

J = ^{12}/_{(4)(2)}

J = ^{12}/_{8}

J = 1.5

Therefore, the **steady state diffusion **is **1.5mol m ^{-2} s^{-1}.**

**Calculating the Diffusion Coefficient when the Steady State Diffusion, the Cross-sectional Area and the Time is Given.**

dC/dx = J x At

Where:

dC/dx = Diffusion Gradient

J = Steady State Diffusion

A = Cross-sectional Area

t = Time

Given an example;

Find the diffusion coefficient when the steady state diffusion is 3, the cross-sectional area is 4 and the time is 9.

This implies that;

J = Steady State Diffusion = 3

A = Cross-sectional Area = 4

t = Time = 9

dC/dx = J x At

dC/dx = 3 x (4)(9)

dC/dx = 3 x 36

dC/dx = 108

Therefore, the **diffusion coefficient **is **108.**

**Calculating the Cross-sectional Area when the Steady State Diffusion, the Diffusion Coefficient and the Time is Given.**

A = ^{dC/dx} / _{J x t}

Where:

A = Cross-sectional Area

J = Steady State Diffusion

dC/dx = Diffusion Gradient

t = Time

Let’s solve an example;

Given that, the steady state diffusion is 12, the diffusion coefficient is 72 and the time is 6.

This implies that;

J = Steady State Diffusion = 12

dC/dx = Diffusion Gradient = 72

t = Time = 6

A = ^{dC/dx} / _{J x t}

A = ^{72} / _{12 x 6}

A = ^{72} / _{72}

A = 1

Therefore, the **cross-sectional area **is **1.**

**Calculating the Time when the Steady State Diffusion, the Diffusion Coefficient and the Cross-sectional Area is Given.**

t = ^{dC/dx} / _{J x A}

Where:

t = Time

J = Steady State Diffusion

dC/dx = Diffusion Gradient

A = Cross-sectional Area

Let’s solve an example;

Find the time when the steady state diffusion is 8, the diffusion coefficient is 40 and the cross-sectional area is 3.

This implies that;

J = Steady State Diffusion = 8

dC/dx = Diffusion Gradient = 40

A = Cross-sectional Area = 3

t = ^{dC/dx} / _{J x A}

t = ^{40} / _{8 x 3}

t = ^{40} / _{24}

t = 1.67

Therefore, the **time **is **1.67s.**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the steady state diffusion

To get the answer and workings of the steady state diffusion using the **Nickzom Calculator – The Calculator Encyclopedia. **First, you need to obtain the app.

You can get this app via any of these means:

**Web** – https://www.nickzom.org/calculator-plus

To get access to the **professional **version via web, you need to **register** and **subscribe **to have utter access to all functionalities.

You can also try the **demo **version via https://www.nickzom.org/calculator

**Android (Paid)** – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator

**Android (Free)** – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator

**Apple (Paid)** – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

Once, you have obtained the calculator encyclopedia app, proceed to the **Calculator Map, **then click on **Materials and Metallurgical **under **Engineering****.**

Now, Click on **Diffusion In Alloying**** **under **Materials and Metallurgical**

Now, Click on **Steady State Diffusion**** **under **Diffusion In Alloying**

The screenshot below displays the page or activity to enter your values, to get the answer for the steady state diffusion according to the respective parameter which is the **Diffusion Gradient (dC/dx), Cross-sectional Area (A) **and **Time (t).**

Now, enter the values appropriately and accordingly for the parameters as required by the **Diffusion Gradient (dC/dx)** is **12**,** Cross-sectional Area (A)** is **4 **and **Time (t)** is **2**.

Finally, Click on Calculate

As you can see from the screenshot above, **Nickzom Calculator**– The Calculator Encyclopedia solves for the steady state diffusion and presents the formula, workings and steps too.