The temperature of a metallic sphere of radius R is increased by a small amount Δ T . If the linear coefficient of thermal expansion of the metal is α , the approximate increase in the volume of the s

Question

The temperature of a metallic sphere of radius R is increased by a small amount Δ T . If the linear coefficient of thermal expansion of the metal is α , the approximate increase in the volume of the sphere is :NEET 2026 (Re-NEET)

TestHub · Accepted Answer

The initial volume of the metallic sphere is $V = \frac{4}{3} π R^{3}$ .

The coefficient of volume expansion $γ$ is related to the linear coefficient of thermal expansion $α$ as $γ = 3 α$ .

The increase in volume $Δ V$ due to a temperature increase $Δ T$ is given by $Δ V = Vγ Δ T$ .

Substituting the values of $V$ and $γ$ , we get:

$Δ V = (\frac{4}{3} π R^{3}) (3 α) Δ T$

$Δ V = 4 π R^{3} α Δ T$

Answer: $4 π R^{3} α Δ T$

Physics - Heat & Thermo Question with Solution | TestHub

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