Thermal Expansion of Solids

Written by Jerry Ratzlaff on . Posted in Thermodynamics

thermal expansion solid 1

Mean depth formula

\(\large{ \Delta l  =      \overrightarrow{\alpha_l}  \; l_i \; \Delta T }\)  (linear expansion) 
\(\large{ \Delta A  = 2\; \overrightarrow{\alpha_l} \;  A_i \; \Delta T }\)  (aerial or superficial expansion) 
\(\large{ \Delta V  =  3\; \overrightarrow{\alpha_l} \; V_i \; \Delta T }\)  (volumetric or cubical expansion) 

Where:

 Units English Metric
\(\large{ \Delta l }\) = length differential \(\large{ in }\) \(\large{ mm }\)
\(\large{ \Delta A }\) = area differential \(\large{ in^2 }\) \(\large{ mm^2 }\)
\(\large{ \Delta V }\) = volume differential \(\large{ in^3 }\) \(\large{ mm^3 }\)
\(\large{ A_i }\) = initial area of object \(\large{ in^2 }\)  \(\large{ mm^2 }\) 
\(\large{ l_i }\) = initial length \(\large{ in }\)  \(\large{ mm }\) 
\(\large{ V_i }\) = initial volume of object \(\large{ in^3 }\)   \(\large{ mm^3 }\)  
\(\large{ \overrightarrow{\alpha_l} }\)   (Greek symbol alpha) = linear thermal expansion coefficient \(\large{ \frac{in}{in\;F} }\) \(\large{ \frac{mm}{mm\;C} }\)
\(\large{ \Delta T }\) = temperature differential  \(\large{ F }\)  \(\large{ C }\)

 

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Tags: Thermal Equations Expansion Equations