How should I calc this heat durability feat?

[IDK3465]

In Minecraft, there is a dimension called the Nether, and it's basically the Minecraft universe's version of hell, you know, fire and brimstone and all that.
Most notably, it's HOT, like, hot enough to instantly vaporize an entire cubic meter of water in a fraction of a second. Despite this, the player and basically any other Mob in the game (except Snow Golems ig) can survive in the Nether without issue.

Unfortunately, we're never given a stated temperature for the Nether in any other media as far as I can tell, so I'm wondering, how exactly would I go about calculating everybody's durability from this? Can I calculate the theoretical temp and go from there, or would that be against the rules? Should I divide the energy/second by the water's surface area and apply that to everyone? Or is there still a method I'm missing here?

 

[MSahla]

Despite this, the player and basically any other Mob in the game (except Snow Golems ig) can survive in the Nether without issue.

Unfortunately, we're never given a stated temperature for the Nether in any other media as far as I can tell, so I'm wondering, how exactly would I go about calculating everybody's durability from this?

Well, if everyone can survive the Nether, which is very hot like you said, wouldn't that be just a Resistance to Heat Manipulation/Extreme Heat?

 

[ByArrow]

Well, if everyone can survive the Nether, which is very hot like you said, wouldn't that be just a Resistance to Heat Manipulation/Extreme Heat?

It can be both

 

[Caol3108]

It can be both

I'm with this ↑

 

[IDK3465]

Well, if everyone can survive the Nether, which is very hot like you said, wouldn't that be just a Resistance to Heat Manipulation/Extreme Heat?

As ByArrow said, it can be both: we have calcs for surviving the surface of the sun as well as surviving lava, so yes, this is a valid durability feat

 

[RSM9976]

In Minecraft, there is a dimension called the Nether, and it's basically the Minecraft universe's version of hell, you know, fire and brimstone and all that.
Most notably, it's HOT, like, hot enough to instantly vaporize an entire cubic meter of water in a fraction of a second. Despite this, the player and basically any other Mob in the game (except Snow Golems ig) can survive in the Nether without issue.

Unfortunately, we're never given a stated temperature for the Nether in any other media as far as I can tell, so I'm wondering, how exactly would I go about calculating everybody's durability from this? Can I calculate the theoretical temp and go from there, or would that be against the rules? Should I divide the energy/second by the water's surface area and apply that to everyone? Or is there still a method I'm missing here?

To calc this you'd need to solve the rate of heat transfer q (W) between the Nether air and the mob you're calcing for. Then you'd convert to joules using the time between damage ticks for Snow Golems. You'll need a 3D transient heat transfer equation to find the temperature of air that fully evaporates ~1 m^3 of water in 1 tick. You'll probably need to use a heat transfer textbook to find the appropriate equations and properties for water/air.

Although I don't think this translates to durability for most mobs. Possible Snow Golem upscale though lol.

 

[IDK3465]

Ok, doing some digging, a lot of people have already attempted to calc the heat of the Nether
The problem is that the results range all the way from 228.88 °C to 261.8 BILLION °C, so honestly, I have no clue what I'm supposed to do here, could be anything for all I know

 

[RSM9976]

Ok, doing some digging, a lot of people have already attempted to calc the heat of the Nether
The problem is that the results range all the way from 228.88 °C to 261.8 BILLION °C, so honestly, I have no clue what I'm supposed to do here, could be anything for all I know

Here's the equation I would use

You could also use the transient lumped system equation which is easier but generally used for small objects. For a 3D cube theta is raised to the power of 3 before solving for temperature.

EDIT: This takes into account the rapid heating but not vaporization like the other posts. This problem more complicated than I thought.

 

[IDK3465]

Ok, since this is clearly a FUCKTON more complicated than I thought it'd be, how about I use the formula the guy on Reddit used as a lowball for the temp? I noticed a few flaws in their values that could bump the feat up a bit anyway, it could probably would get within tier 8 still

 

[RSM9976]

Ok, since this is clearly a FUCKTON more complicated than I thought it'd be, how about I use the formula the guy on Reddit used as a lowball for the temp? I noticed a few flaws in their values that could bump the feat up a bit anyway, it could probably would get within tier 8 still

You're kinda lucky because yeah you'd be better off using those formulas. I just realized that the equations I posted uses the thermal diffusivity alpha, which is like 10^-7 m^2/s for water. If you do the math with it, my equation wont work, as the diffusivity makes it physically impossible for any heat to reach the center of the water in that short time frame.

Alternatively, I think you can use the lumped system approach now, which gives you a lower bound for the temperature.

 

[AyOgUyS]

The problem is that the results range all the way from 228.88 °C to 261.8 BILLION °C

"Mach 5 to lightspeed" type range

 

[IDK3465]

Actually, I think I'll use either Newton's law of cooling or the Stefan–Boltzmann law, though I'm unsure which is better for this case, I'd like some advice here

 

[RSM9976]

Actually, I think I'll use either Newton's law of cooling or the Stefan–Boltzmann law, though I'm unsure which is better for this case, I'd like some advice here

Stefan-Boltzmann law is radiation only. Most of your heat will come from convection. Newton's law of cooling accounts for both convection and radiation assuming the correct k value is used. Lumped system equation lets you calc k yourself, and you can include radiation via h = h_conv + h_rad if you'd like.

Also keep in mind Newton's law of cooling is 1D and its just:
theta_x = e^-kt

 

[IDK3465]

Stefan-Boltzmann law is radiation only. Most of your heat will come from convection. Newton's law of cooling accounts for both convection and radiation assuming the correct k value is used. Lumped system equation lets you calc k yourself, and you can include radiation via h = h_conv + h_rad if you'd like.

Also keep in mind Newton's law of cooling is 1D and its just:
theta_x = e^-kt

I have been kinda sleep deprived for the past couple of days, and the sheer number of variables I need to figure out here is giving me an aneurism
Is it at all possible for you to fill out the thing for me? You seem to know this shit way better than I do anyway

 

[RSM9976]

I have been kinda sleep deprived for the past couple of days, and the sheer number of variables I need to figure out here is giving me an aneurism
Is it at all possible for you to fill out the thing for me? You seem to know this shit way better than I do anyway

Here's a rough example to help you start. I strongly recommend a thermodynamics textbook lmao.

h (air, free convection, no radiation): Varies, I'll guess 10 W/(m^2K)
A_s (surface area): 1 m^2
Rho (density of water): 1000 kg/m^3
V (Volume of water): 1 m^3
c_p (specific heat of water): Varies, guess 4184 J/(kg K)
t (time): 1/20 s
T_i = 20, T = 100
Newton's law of cooling/lumped system analysis:

Theta_x = e^-bt
b = h A_s / (rho V c_p)

Product rule:

Theta = Theta_x Theta_y Theta_z = Theta_x^3

Eq for nondimensional temperature Theta: Given in image I sent above.

Plug everything in and you get
T_inf = ~2e8 °C.

No vaporization no radiation.

 

[IDK3465]

Here's a rough example to help you start. I strongly recommend a thermodynamics textbook lmao.

h (air, free convection, no radiation): Varies, I'll guess 10 W/(m^2K)
A_s (surface area): 1 m^2
Rho (density of water): 1000 kg/m^3
V (Volume of water): 1 m^3
c_p (specific heat of water): Varies, guess 4184 J/(kg K)
t (time): 1/20 s
T_i = 20, T = 100
Newton's law of cooling/lumped system analysis:

Theta_x = e^-bt
b = h A_s / (rho V c_p)

Product rule:

Theta = Theta_x Theta_y Theta_z = Theta_x^3

Eq for nondimensional temperature Theta: Given in image I sent above.

Plug everything in and you get
T_inf = ~2e8 °C.

No vaporization no radiation.

Holy shit, thank you SO much for your help, I'll make sure to refine this and put it in a calc blog later once I have the time
Sorry for taking away so much of your spare time :[

 

[AyOgUyS]

Holy shit, thank you SO much for your help, I'll make sure to refine this and put it in a calc blog later once I have the time
Sorry for taking away so much of your spare time :[

we need a calc ppl appreciation day or smth cuz they genuinely hard carry us scalers' asses

 

[IDK3465]

Ok, I recalculated the temp and got 11157114.5481°C
I feel like I messed something up

I think I might just do the method that guy on Reddit used as a low end because no way in hell is this getting accepted

 

[IDK3465]

Ok, I recalculated the temp and got 11157114.5481°C
I feel like I messed something up

I think I might just do the method that guy on Reddit used as a low end because no way in hell is this getting accepted

Ok, the Reddit guy's method gave me 3446.4°C, much more agreeable imo

 

[IDK3465]

Ok, the Reddit guy's method gave me 3446.4°C, much more agreeable imo

WAIT, I forgot to use the total energy released every second, it's actually 74118°C

Using max energy intake since that seems to be what our profiles typically use for feats like this:
3470*342*74118 = 87958795320 joules or 21.0227 Tons of TNT (8-B)

MINECRAFT LOW TIER UPSCALE BABY LET'S GO