Question

An iron railway line is 30m long at a temperature of 27oC. What would be the length of the 

railway line when the temperature increases to 57oC? The coefficient of linear expansion of 

iron is 1.2 x 10-5 oC-1

Answer 1

Solution.

$L=30m;$

$t_1=27^oC;$

$t_2=57^oC;$

$\alpha=1.2\sdot10^{-5}C^{-1};$

$L_0=\dfrac{L}{1+\alpha \Delta T};$

$L_0=\dfrac{30}{1+1.2\sdot10^{-5}\sdot7}=29.99m;$

$L1=L_0(1+\alpha \Delta T);$

$L_1=29.99(1+1.2\sdot10^{-5}\sdot37)=30.003m;$

Answer: $L_1=30.003m.$