ABSOLUTE UNITS:
plus 460 to go from F to Rankine (R)
plus 14.7 to go from PSIG to PSIA
Conditions:
Field temperature at half time: 45 F
Regulation ball pressure: 13.0 psig. (actually 12.5 to 13.5 pig)
Depressed ball pressure: 10.5 psig. (assumed. Going for a 2.5 psi deflation)
Room temperature required: xx F
Revised conditions:
T2a = 45 + 460
T1a = T1 + 460
P1 = 13.0 psig + 14.7 = 27.7 psia
P2 = 10.5 psig + 14.7 = 25.2 psia
Ideal gas equation is : PV=nRT
Rearrange to: (PV/nRT)1=(PV/nRT)2
Equation:
T2 = (T1 + 460 ) * (P1/P2) - 460
P1/P2 = 24.7/24.7 = 1.10 (So 10% hotter is required)
T2a = 505 R * 1.1 = 555 R
T2 = T2a - 460 = 555 - 460 = 95 F
So the a temperature change scheme requires a room 50 F hotter than field temperature.
It also requires that the balls be checked in the hotter room.
To avoid the same advantage for the other team, you need to have their ball room at field temperature.
so, to keep it simple, just pump them up outside before the game.