# Thermal Expansion Law

1. An iron railroad rail is 2100 ft long when the temperature is 25°C. What is its length when the temperature is -15°C?

2. A copper vat is 12m long at room temperature (20°C). How much longer is it when it contains boiling water at 1atm pressure?

The law of thermal expansion for relative small intervals of temperatures is

$\Delta(L)/L0 = \alpha*\Delta(T)$

where delta is the variation, L the length, T the temperature and $\alpha$ the coefficient of thermal linear expansion.

$\alpha_{iron} = 11.1*10^{-6} (1/Celsius)$

$\alpha_{Cu} = 17*10^{-6} (1/Celsius)$

$\Delta(L) = L0*\alpha_{iron}*(25+15) =2100*11.1*10^{-6}*40 =0.9324 foot$
$L = L0+\Delta(L) =0.9324+2100 =2100.9324 feet = 636.35 m$
$\Delta(L) =L0*\alpha_{Cu}*(100-20) =12*17*10^{-6} *80 =0.01632 m$
$L = L0+\Delta(L) =12 +0.01632 =12.01632 m$