Each side of a box made of metal sheet in cubic shape is ' a ' at room temperature 'T',

Question:

Each side of a box made of metal sheet in cubic shape is ' $a$ ' at room temperature 'T', the coefficient of linear expansion of the metal sheet is ' $\alpha^{\prime}$. The metal sheet is heated uniformly, by a small temperature $\Delta \mathrm{T}$, so that its new temperature is $\mathrm{T}+\Delta \mathrm{T}$. Calculate the increase in the

volume of the metal box-

  1. $\frac{4}{3} \pi a^{3} \alpha \Delta T$

  2. $4 \pi \mathrm{a}^{3} \alpha \Delta \mathrm{T}$

  3. $3 a^{3} \alpha \Delta T$

  4. $4 \mathrm{a}^{3} \alpha \Delta \mathrm{T}$


Correct Option: , 3

Solution:

(3)

volume expansion $\gamma=3 \alpha$

$\frac{\Delta \mathrm{V}}{\mathrm{V}}=\gamma \Delta \mathrm{T}$

$\Delta \mathrm{V}=\mathrm{V} \cdot \gamma \Delta \mathrm{T}$

$\Delta \mathrm{V}=\mathrm{a}^{3} \cdot 3 \alpha \Delta \mathrm{T}$

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