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A spherical shell of copper is completely filled with a liquid at a temperature t°C. The bulk modulus of the liquid is K and coefficient of volume expansion is $γ$ . If the temperature of the liquid and the shells increased by $∆ T$ , then the outward pressure $∆ p$ on the shell that results from the temperature increase is given by ( $α$ is the coefficient of linear expansion of the material for the shell):

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$K (3 α - γ) ΔT$

$γ (3 α - K) ΔT$

$3 α (K - γ) ΔT$

$K (γ - 3 α) ΔT$

answer is A.

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Detailed Solution

$\begin{array}{l} k = \frac{Δp}{ΔV / V} \Rightarrow Δp = k \frac{ΔV}{V} \\ \frac{ΔV}{V} = 3 α ∆ T - γ ∆ T \\ Δp = k \frac{ΔV}{V} = k ∆ T (γ - 3 α) \end{array}$

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