A soap bubble expands isothermally and its radius doubles. The work done by surface tension during this expansion is: 

When a soap bubble expands, work is done against surface tension to increase the surface area. A soap bubble has two surfaces (inner and outer), so total surface area is twice that of a single sphere. Let:

• Initial radius =
• Final radius = 2R
• Surface tension = T

Initial surface area of one surface = 4πR² Since there are two surfaces, total initial area: A1 = 2. 4πR² = 8πR² Final surface area with radius 2R: A2 = 2. 4π(2R)² = 32πR² Work done by surface tension Work done = T ⋅ ΔA = T ⋅ (A2 – A1) W = T.(32πR² - 8πR²) W = 24πR²T