Can Blood Balls Cool Faster in Vacuum or Air?

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    Ball Cooling Vacuum
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Discussion Overview

The discussion revolves around the cooling rates of a hypothetical blood ball in two different environments: vacuum and air. Participants explore the theoretical implications of heat loss through conduction and radiation, considering the specific conditions of the scenario.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant proposes calculating the cooling time of a blood ball with a radius of 200 cm and an initial temperature of 310 K, aiming to reach approximately 285 K in both vacuum and air.
  • Another participant suggests using empirical measurements to estimate heat loss in air at about 10 W/m²*K, noting that this value changes as the temperature difference decreases.
  • A participant calculates the total heat released from human blood, estimating it to be around 3.65 × 10^15 J based on specific heat capacity and mass, and expresses interest in modeling this scenario using computational tools.
  • Using the provided values, one participant estimates an initial energy loss of 125 MW, leading to a cooling timescale of approximately 338 days, with a note that the temperature decay may follow an exponential trend over a year.
  • A light-hearted comment is made questioning the motivation behind the scenario, suggesting it relates to vampire interests due to the context of blood and the proximity to Halloween.

Areas of Agreement / Disagreement

Participants present various calculations and models, but there is no consensus on the exact cooling times or methods, indicating multiple competing views and unresolved aspects of the discussion.

Contextual Notes

Participants rely on different assumptions regarding heat transfer rates and environmental conditions, which may affect the accuracy of their calculations. The discussion does not resolve the complexities involved in modeling the cooling process.

nehorlavazapal
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Hi,

If we took the blood of all people here on Earth and made a ball of it (r=200, T = 310 K) how long would it take for it to cool down to ~ 285 K in vacuum (absent of sunglight)? How long would it take to cool down in air, with reasonable conduction speeds?
 
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empirical measurements can be used to approximate this to something like 10 W/m^2*K in air, where the K comes from the temperature difference between the ball and the air.

So for example your initial heat loss would be (4/3)*pi*200^2*10*(310 - 285), surface area times 10 times temperature difference. As the body cools this heat loss will drop as the surface temperature (310) will not be a constant, so you're solving a differential equation here.

Conductive effects are usually a lot higher, radiation will be a lot lower.

The link between heat flux and time to steady-state temperature is entirely governed by the heat capacity of the object.
 
The total heat released will be 4180 J per kg × 25 × 35 billion = 3,65 × 10^15 J.

Wow, that's a lot of heat stored in human blood! S = 502 000 m^2. So in total each m^2 would need to radiate/conduct 7,2×10^9 J. That's a lot. Can somebody offer a model in some kind of computer program? This is basic stuff, so many programs should do the trick!
 
Using your values, the initial energy loss is 10W/(m^2*K) * 25K * 500 000m^2 = 125MW.
Assuming the interior conducts much better than the air/bubble surface, this gives a timescale of 7.2GJ/(125MW) = 338 days.

Assuming the air around the ball won't heat too much, this leads to an exponential decay of the temperature with a timescale of roughly one year.
WolframAlpha Plot (x in days, y in K)

Why human blood?
 
Must be a vampire or represent vampire related interests. After all, it's only a fortnight to Halloween!
 

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