We from gas equation:
PV=mRT
Where:
P is pressure (1 torr = 0.013N/cm2)
V is the volume of the balloon
m is the mass of gas in the balloon (constant)
R is universal gas constant divided by mean molar wt of air (about 28 g/mol) T is thermodynamic temperature (T in Kelvin; T=273 + t (in deg C)
So, For given values in gas equation and assuming we have 1 gm of gas in the balloon, we get:
28 * V = 1 * R * (-39+273)
or, 28 * 0.013 * V = 1 * 28 * 324
or, V = 324 / 0.013 cm^3
or, V = 18000 cm^3
