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A liquid of volumetric thermal expansion coefficient $200 \times 10^{- 6} / ° C$ and bulk modulus = $1.2 \times 10^{9} P a$ is filled in a spherical tank of negligible heat expansion coefficient. Its radius is 25 cm and wall thickness is 2 mm. When the temperature of the liquid is raised by $20 ° C$ , find the tensile stress developed (in MPa) in the wall of the tank?

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Detailed Solution

$| d P | = β | \frac{d v}{V} |$
Balancing force, $d P π R^{2} = σ 2 π R t \Rightarrow σ = \frac{d P}{2} \frac{R}{t} = \frac{β γ Δ θ R}{2 t}$

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Where $β$ =bulk modulus
$γ$ = coefficient of thermal expansion
$Δ θ$ = change in temperature
R = radius of sphere
t = thickness of sphere.

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