A spherical bubble has surface tension S and contains ideal gas with γ = 5/3. At atmospheric pressures Pₐ₁ and Pₐ₂, its states are (r₁, T₁) and (r₂, T₂). Select the correct thermodynamic/surface-tension relations.
Select all that apply

Question

A spherical bubble has surface tension S and contains ideal gas with γ = 5/3. At atmospheric pressures Pₐ₁ and Pₐ₂, its states are (r₁, T₁) and (r₂, T₂). Select the correct thermodynamic/surface-tension relations.

Select all that apply

G1 Physics · Accepted Answer

Step 1: Use surface-energy/pressure relations: ΔP = 2T/R for a liquid drop or 4T/R for a soap bubble, capillary rise h = 2T cosθ/(ρgr), and surface energy = TΔA. Step 2: Apply force or energy balance to the stated radii and surface areas. Applying these relations to the given data gives C: If perfectly conducting with negligible atmospheric-temperature change, (r₁/r₂)³ = [Pₐ₂ + 4S/r₂]/[Pₐ₁ + 4S/r₁].; D: If perfectly insulated, (T₂/T₁)^(5/2) = [Pₐ₂ + 4S/r₂]/[Pₐ₁ + 4S/r₁].. Final answer: CD.

A spherical bubble has surface tension S and contains ideal gas with γ = 5/3. At atmospheric pressures Pₐ₁ and Pₐ₂, its states are (r₁,T₁) and (r₂,T₂). Select the correct thermodynamic/surface-tension relations.