Answer:
The steel rod should be cooled by 99.88°C
Explanation:
To solve this exercise we require the thermodynamic concept of thermal expansion.
Here it is necessary to have the coefficient of thermal expansion for steel, since the formula to calculate is:
[tex]\Delta L = \alpha L_0 \Delta T[/tex]
Where
ΔL represents the change in length,
[tex]L_0[/tex] is the initial length,
α is the coefficient of thermal expansion
ΔT the change in temperature.
α of the steel is [tex]12 * 10 ^{-6} C^{-1}[/tex]
The longitudinal change of our material is of
[tex]\Delta L = 2.0024cm-2.0cm = 0.0024cm= 2.4*10^{-5}m[/tex]
[tex]L_0 = 2.0024cm= 2.0024*10^{-2}m[/tex]
Replacing,
[tex]\Delta L = \alpha L_0 \Delta T[/tex]
[tex]2.4*10^{-5}=12*10^{-6}(2.0024*10^-2)\Delta T[/tex]
Solving to [tex]\Delta T[/tex],
[tex]\Delta T = \frac{2.4*10^{-5}}{12*10^{-6}(2.0024*10^-2)}[/tex]
[tex]\Delta T = 99.88\°C[/tex]
Therefore the steel rod should be cooled by 99.88°C
