A soap bubble of radius 1 cm is kept in vacuum. It is filled with diatomic gas. Surface tension = 0.5 N / m . Find the heat required Q (in J ) to be given to double it's radius. Neglect the heat

Question

A soap bubble of radius 1 cm is kept in vacuum. It is filled with diatomic gas. Surface tension = 0.5 N / m . Find the heat required Q (in J ) to be given to double it's radius. Neglect the heat capacity of soap film. Initial temperature = 300 K .

TestHub · Accepted Answer

P = r 4 S ​ V = 3 4 ​ π r 3 n = RT P V ​ = 0.01 × 3 25 ​ × 300 4 × 0.5 × 3 4 ​ × π ( 0.01 ) 3 ​ = 15 16 π ​ × 1 0 − 5 P V 3 1 ​ = Constant C = C V ​ + 1 − x R ​ = 4 R T V − 3 2 ​ = Constant T 0 ​ ( 3 4 ​ π × 1 3 ) − 3 2 ​ = T ( 3 4 ​ π × 2 3 ) − 3 2 ​ T = 1200 K Q = n C Δ T Q = 15 16 π ​ × 1 0 − 5 × 4 × 3 25 ​ × 900 = 1 J

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