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 '$\alpha$'. The metal sheet is heated uniformly, by a small temperature $\Delta$T, so that its new temperature is T + $\Delta$T. Calculate the increase in the volume of the metal box.
Solution
We know that, $\gamma = 3\alpha$ .... (i)<br/><br/>where, $\alpha$ is the coefficient of linear expansion and $\gamma$ is the coefficient of volume expansion. <br/><br/>We know that,<br/><br/>${{\Delta V} \over V} = \gamma \Delta T$<br/><br/>$\Rightarrow {{\Delta V} \over V} = 3\alpha \Delta T$ [from Eq. (i)]<br/><br/>$\Delta V = 3{a^3}\alpha \Delta T$ [ $\because$ volume of cube = a<sup>3</sup> ]
About this question
Subject: Physics · Chapter: Thermodynamics · Topic: Zeroth and First Law
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