So I was walking home from the local shop, backpack filled with all that i neede for the weekend, including some beers! 🍻

BUT! Going home made me think, would really be nice if the where chilled down as fast as possible.

So when I got home I asked my local hosted LLM (Large Language Model) in this case its the new LLM from META (Facebook). llama3, the one I use for how as I clearly dont have the hardware for going all in is: llama3:8b-instruct-q6_K.

Here is how it went!⌗

I have a physics question for you:

If I have a liquid in a container and need to lower its temperature from room temperatur (20°C).

What is faster then:

  • Putting it in a room at 5°C
  • Putting it in a room at -18°C

Please explain the math / physics behind your answer and output it as markdown.

Lets see what our local house robot replied:⌗

A nice question!

Let’s dive into the physics of heat transfer.

Heat Transfer Mechanisms

There are three primary mechanisms for heat transfer:

  1. Conduction: Heat transfer between objects in direct physical contact, through molecules colliding with each other.
  2. Convection: Heat transfer through the circulation of fluids (liquids or gases) due to density changes caused by temperature differences.
  3. Radiation: Heat transfer through electromagnetic waves, such as infrared radiation.

Heat Transfer Coefficients

Each mechanism has a corresponding heat transfer coefficient, which represents the rate of heat transfer per unit area and temperature difference:

  1. Conduction: k (W/m·K) - thermal conductivity
  2. Convection: h (W/m²·K) - convective heat transfer coefficient
  3. Radiation: εσ (W/m²·K⁴) - Stefan-Boltzmann constant multiplied by the emissivity of the surface

Heat Transfer Rate

The heat transfer rate (Q) is proportional to the temperature difference (ΔT) and the heat transfer coefficient:

  1. Conduction: Q = k \* A \* ΔT / L (W)
  2. Convection: Q = h \* A \* ΔT (W)
  3. Radiation: Q = εσ \* A \* (T² - T'²) (W)

Where:

  • A: surface area
  • L: thickness of the material (for conduction only)
  • T and T': temperatures of the two objects

Your Question

You want to lower the temperature of a liquid from 20°C to a lower temperature. To do this, you’ll need to remove heat from the system.

Now, let’s compare the heat transfer rates for each scenario:

Scenario 1: Room at 5°C⌗

  • Temperature difference (ΔT): 15°C (20°C - 5°C)
  • Heat transfer rate (Q) through conduction and radiation:
    • Conduction: k \* A \* ΔT / L
    • Radiation: εσ \* A \* (20² - 5²)
  • Heat transfer rate through convection: h \* A \* ΔT

Scenario 2: Room at -18°C⌗

  • Temperature difference (ΔT): 38°C (20°C - (-18°C))
  • Heat transfer rate (Q) through conduction and radiation:
    • Conduction: k \* A \* ΔT / L
    • Radiation: εσ \* A \* (20² - (-18)²)
  • Heat transfer rate through convection: h \* A \* ΔT

Comparison

The key is to find the temperature difference (ΔT) and heat transfer rates for each scenario. Since we’re dealing with a liquid, conduction and radiation will play a minor role in heat transfer. Convection will be the dominant mechanism.

Scenario 1 has a smaller temperature difference (ΔT = 15°C) compared to Scenario 2 (ΔT = 38°C). This means that Scenario 1 will have a lower heat transfer rate through conduction and radiation.

However, Scenario 1 also benefits from a higher convective heat transfer coefficient (h) due to the larger temperature difference between the liquid and the surrounding air. This is because there is more buoyancy-driven circulation in the air, which enhances heat transfer.

Conclusion

After analyzing the physics of heat transfer, we can conclude that:

Scenario 1: Putting the liquid in a room at 5°C will be faster than Scenario 2: Putting the liquid in a room at -18°C.

The smaller temperature difference and higher convective heat transfer coefficient in Scenario 1 lead to a more efficient heat transfer process, resulting in a faster cooling of the liquid.

So thats it? In the fridge the go⌗

Interesting and not something you would easy get from a single Google search, LLMs are tools and we shall not fear the world of AI and machine learning. We need to learn that not everything is a hammer and we aint the nails.

Use the right tool for the job and things will be OK.