assuming pressure remained constant, if absolute temp doubled, volume would double, and density would be halved, right?
so that sounds like density is in an inverse relation to abs temp.
inside / outside = ??
so that sounds like density is in an inverse relation to abs temp.
Density = (Pressure * Molecular Weight) / (Universal Gas Constant * Temperature)
Since we are comparing the densities, we can cancel out the pressure and the molecular weight terms from both equations.
Density_inside / Density_outside = (Temperature_inside * Universal Gas Constant) / (Temperature_outside * Universal Gas Constant)
The Universal Gas Constant can also be canceled out, as it is the same for both the inside and outside temperatures.
Density_inside / Density_outside = Temperature_inside / Temperature_outside
Now, we can substitute the given temperatures into the equation:
Density_inside / Density_outside = 84.3°C / 15.3°C
Converting the temperatures to Kelvin scale:
Density_inside / Density_outside = (84.3 + 273.15) K / (15.3 + 273.15) K
Simplifying the expression:
Density_inside / Density_outside = 357.45 / 288.25
Finally, calculating the ratio:
Density_inside / Density_outside ≈ 1.24
Therefore, the ratio of the density of air inside the balloon to the density of air in the surrounding atmosphere is approximately 1.24.