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If...
"A" is the mass of air (standard air composition and pressure)
"I" is the mass of ice
"V" is the volume of the box where the change of heat happens (no heat interaction with out of the box)
"Ta" is the temperature of the air
"Ti" is the temperature of the ice
Ta > Ti
(Ta - Ti) < 10

Which is the formulas to know the balance temperature and which one to know how much ice has melted (if it melt)?
And it's possible to know even how much time it will take to reach balance temperature? (this is not much important to me, just if you'd like to...)

Thanks a lot in advance ^^

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closed as off-topic by tpg2114 May 18 at 11:20

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  • $\begingroup$ Do we assume Ta = Ti ? $\endgroup$ – Solar Mike May 18 at 10:52
  • $\begingroup$ We assume Ta > Ti $\endgroup$ – Michele Giglio May 18 at 10:54
  • $\begingroup$ And that difference is 10, 20, 200 or 2000? $\endgroup$ – Solar Mike May 18 at 10:56
  • $\begingroup$ Assume less than 10 $\endgroup$ – Michele Giglio May 18 at 10:58
  • $\begingroup$ Edit this info into the question so it is easy for people to read. $\endgroup$ – Solar Mike May 18 at 11:01
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It’s not clear what you are asking. But if “10” is 10 C, and assuming that the ice starts at 0 C at atmospheric pressure then the heat required to melt all the ice will be

$$Ih_v$$

Where $h_v$ is the latent heat of fusion of water.

That in turn would have to equal

$$AC_{P}\Delta T$$

Where $C_P$ is the specific heat of air at constant pressure.

Setting the two equal will give you the required $\Delta T$ of the air to melt all the ice. If it’s equal to or greater than 10 C, all the ice won’t melt. If it’s less than 10 C you will need to know the actual initial temperature of the air.

Hope this helps.

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