Question 347: Thermodynamics & KTG

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 '$\alpha$'. 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.

Accepted Answer

We know that, $\gamma  = 3\alpha $ .... (i)
where, $\alpha$ is the coefficient of linear expansion and $\gamma$ is the coefficient of volume expansion.
We know that,
${{\Delta V} \over V} = \gamma \Delta T$
$ \Rightarrow {{\Delta V} \over V} = 3\alpha \Delta T$ [from Eq. (i)]
$\Delta V = 3{a^3}\alpha \Delta T$ [ $\because$ volume of cube = a
3
]

Answer

3a
3
$\alpha$$\Delta$T

Answer

4$\pi$a
3
$\alpha$$\Delta$T

Answer

${{4 \over 3}}$$\pi$a
3
$\alpha$$\Delta$T

Answer

4a
3
$\alpha$$\Delta$T

Thermodynamics & KTG

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