# Initial Temperature

Written by Jerry Ratzlaff on . Posted in Thermodynamics

## Initial Temperature formulas

$$\large{ T_i = T_f - \frac{ l_f \;- \; l_i }{ \overrightarrow{\alpha_l} \; l_i } }$$     (linear thermal expansion coefficient)

$$\large{ T_i = T_f - \frac{ v_f \;- \; v_i }{ \alpha_v \; v_i } }$$     (volumetric thermal expansion coefficient)

Symbol English Metric
$$\large{ T_i }$$ = initial temperature $$\large{ F }$$ $$\large{ C }$$
$$\large{ l_f }$$ = final length $$\large{ in }$$ $$\large{ mm }$$
$$\large{ l_i }$$ = initial length $$\large{ in }$$ $$\large{ mm }$$
$$\large{ \overrightarrow{\alpha_l} }$$   (Greek symbol alpha) = linear thermal expansion coefficient $$\large{ \frac{in}{in\;F} }$$ $$\large{ \frac{mm}{mm\;C} }$$
$$\large{ T_f }$$ = final temperature $$\large{ F }$$ $$\large{ C }$$
$$\large{ v_f }$$ = final velocity $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$
$$\large{ v_i }$$ = initial velocity $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$
$$\large{ \alpha_v }$$  (Greek symbol alpha) = volumetric thermal expansion coefficient $$\large{ \frac{in^3}{in^3\;F} }$$ $$\large{ \frac{mm^3}{mm^3\;C} }$$