A balloon carries a total load of 185 kg at normal pressure and temperature of 27°C. What load will the balloon carry on rising to a height at which the barometric pressure is 45 cm of Hg and the temperature is -7°C. Assuming the volume constant?

Solution

Physics sir · 4 steps

The lift is just the weight of air the balloon pushes aside, so track how air density changes with P and T.

1. What sets the load. By Archimedes' principle, the upthrust equals the weight of air displaced. The volume is fixed, so the load the balloon can carry is proportional to the density of the outside air.
2. Density of air. From PV = nRT, the density of a gas is ρ = PM/RT, so ρ ∝ P/T. Temperatures must be in kelvin: T₁ = 300 K and T₂ = 266 K.

   L₂/L₁ = ρ₂/ρ₁ = P₂/P₁×T₁/T₂

3. Put in numbers. Normal pressure is 76 cm of Hg. So L₂ = 185 × 45/76 × 300/266 = 185 × 0.5921 × 1.1278 = 185 × 0.6678.
4. So. L₂ ≈ 123.54 kg, which is option (d).

The idea to keep. For a fixed-volume balloon, the load scales with outside air density, and ρ ∝ P/T. Always convert temperatures to kelvin before taking the ratio.

Answer from the NTA final answer key. Solution by PrepWiser.