# Derivation of boiling an egg formula using laplace transformation

• crazystuff
In summary, the conversation is about finding the formula for boiling a perfect soft-boiled egg using Laplace Transformation. The person asking for help has done background research on the materials and energy transfer involved, but is struggling with the mathematical aspect. They are looking for assistance or any resources that could help them with this challenging subject. Someone else in the conversation asks about the assumptions being made, such as the distribution of the egg's mass and its shape.
crazystuff
I have been set a challenge to derive the formula for boiling a “perfect” soft-boiled egg, (essentially a thermal diffusion equation), in terms of the mass of the egg, the specific heat capacity and thermal conductivity of an egg, the initial temperature of the egg and the temperature of the boiling water using Laplace Transformation. Is it even possible, if so, is it published anywhere or does anyone know someone who has succeeded so that I can work through it?

I have done a lot of background reading about the materials and make up of an egg and the transfer of heat and energy. I have done my introduction, but unfortunately I am not very good at mathematics. Therefore I have taught myself the Laplace transformation, but now I am completely stuck. Can anyone point me in the right direction please or is there anyone else I can contact who might be able to help me. I would be very grateful for any help given to me on this challenging subject.

Many Thanks

what asumptions are you making? the mass of the egg is evenly distributed through out the egg? or are you seperating the yoke? is this egg spherical?

## 1. How is Laplace transformation used in the derivation of boiling an egg formula?

Laplace transformation is a mathematical tool used to transform a function from the time domain to the frequency domain. In the context of boiling an egg, it is used to represent the temperature of the egg as a function of time.

## 2. What is the significance of using Laplace transformation in this derivation?

Using Laplace transformation allows us to solve the differential equation for the temperature of the egg in a simpler way, as it can be represented as a algebraic equation in the frequency domain. This makes it easier to find the solution for the temperature at any given time.

## 3. Can Laplace transformation be applied to other cooking processes?

Yes, Laplace transformation can be applied to any process that involves a change in temperature over time. It is commonly used in cooking, chemical reactions, and other scientific fields.

## 4. Is there a specific formula for boiling an egg using Laplace transformation?

Yes, the formula for boiling an egg using Laplace transformation is known as the "Laplace transformed egg formula" and is given by: T(s) = (Tb - To) * (1 - e^(-ks))/(s + k), where T(s) is the temperature at time t, Tb is the boiling water temperature, To is the initial egg temperature, k is a constant related to the thermal conductivity of the egg, and s is the Laplace variable.

## 5. Are there any limitations to using Laplace transformation in this derivation?

One limitation is that Laplace transformation assumes a constant thermal conductivity, which may not always be the case in real-life scenarios. Additionally, the formula may not accurately predict the temperature of the egg if the heat source is not constant or if the egg is not of a standard size or shape.

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