(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If a solid material is in the form of a block rather than a rod, its volume will grow larger when it is heated, and a coefficient of volume expansion beta defined by

[tex]\beta = \frac{{{V_2} - {V_1}}}{{{V_1}\left( {{t_2} - {t_1}} \right)}}[/tex]

may be quoted. Here [tex]{V_1}[/tex] and [tex]{V_2}[/tex] are the initial and final volumes of the block, and [tex]{t_1}[/tex] and [tex]{t_2}[/tex] are the initial and final temperatures. Find the relation between the coefficients [tex]\alpha[/tex] and [tex]\beta[/tex].

2. Relevant equations

[tex]\alpha = \frac{{{L_2} - {L_1}}}{{{L_1}\left( {{t_2} - {t_1}} \right)}}[/tex]

3. The attempt at a solution

I'm assuming I need to set [tex]{V_1} = {L_1}{W_1}{H_1}[/tex] and [tex]{V_2} = {L_2}{W_2}{H_2}[/tex]

and attempt to extract [tex]\frac{{{L_2} - {L_1}}}{{{L_1}\left( {{t_2} - {t_1}} \right)}}[/tex] from [tex]\frac{{{L_2}{W_2}{H_2} - {L_1}{W_1}{H_1}}}{{{L_1}{W_1}{H_1}\left( {{t_2} - {t_1}} \right)}}[/tex]

I've only gotten so far:

[tex]{W_1}{H_1}B = \frac{{{L_2}{W_2}{H_2} - {L_1}{W_1}{H_1}}}{{{L_1}\left( {{t_2} - {t_1}} \right)}}[/tex]

but I can't figure out the rest of the algebraic manipulation.

Is this possible, or am I going about the problem incorrectly?

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# Relationship between coefficients of linear and volume expansion

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