The air inside a hot air balloon has an average temperature of 84.3°C. The outside air has a temperature of 15.3°C. What is the ratio of the density of air in the balloon to the density of air in the surrounding atmosphere?
inside / outside = ??
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.
To find the ratio of the density of air inside the balloon to the density of air in the surrounding atmosphere, we can use the ideal gas law. The ideal gas law relates the density, temperature, and pressure of a gas. The density can be calculated using the formula:
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.