Temperature 61484

The air bubble at the bottom of the lake at a depth of h = 21 m has a radius r1 = 1 cm at a temperature of t1 = 4 °C. The bubble rises slowly to the surface, and its volume increases. Calculate its radius when it reaches the lake's surface, with a temperature of t2 = 27 °C. Atmospheric pressure is b = 0.1 MPa, water density = 1030 kg. m-3. Do not take surface tension into account.

Correct answer:

r2 =  1.0269 cm

Step-by-step explanation:

h1=21 m T1=4°CK=4+273.16 K=277.16 K r1=1 cm m=1:100  m=0.01 m ρ=1030 kg/m3 V1=34 π r13=34 3.1416 0.0134.1888106 m3  T2=27°CK=27+273.16 K=300.16 K p2=0.1 106=100000 Pa  p1=p2+m ρ h1=100000+m 1030 21=100000 Pa   T1p1 V1 = T2p2 V2  V2=p2 T1p1 V1 T2=100000 277.16100000 4.1888106 300.164.5364106 m3  V2 = 34 π r23  x=34π3 V2=34 3.14163 4.53641060.0103 m  r2=x cm=x 100  cm=0.0103 100  cm=1.027 cm=1.0269 cm

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