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Materials expand when heated. Consider a metal rod of length L0 at temperature T0. If the temperature is changed by an amount ΔT, then the rod’s length changes by ΔL=????L0ΔT, where ???? is the thermal expansion coefficient. For steel, ????=1.24×10−5∘C−1. (a) A steel rod has length L0=70cm at T0=70∘C. What is its length at T=110∘C?

Respuesta :

Answer:

[tex]\Rightarrow L=70 .03472 cm[/tex]

Explanation:

For convenience, let's represent the thermal expansion coefficient by [tex]\alpha[/tex], i.e. [tex]????=\alpha[/tex].

Given that, for steel [tex]\alpha =1.24\times 10^{-5}[/tex] °[tex]C^{-1}[/tex],

initial length, [tex]L_0=70 cm[/tex], initial temperature, [tex]T_0=70[/tex] °[tex]C[/tex], and the final temperature, [tex]T=110[/tex] °[tex]C[/tex].

Let the length of the rod at [tex]T=110[/tex] °[tex]C[/tex] be [tex]L[/tex].

Now, change in length, [tex]\Delta L=\alpha L_0 \Delta T[/tex]

[tex]\Rightarrow \Delta L=\alpha L_0 (T-T_0)[/tex]

[tex]\Rightarrow L-L_0=1.24\times 10^{-5}\times 70 (110-70)[/tex]

[tex]\Rightarrow L-70=1.24\times 10^{-5}\times 70 \times 40[/tex]

[tex]\Rightarrow L=70 + 0.03472 cm[/tex]

[tex]\Rightarrow L=70 .03472 cm[/tex]

Hence, the length of the rod at [tex]T=110[/tex] °[tex]C[/tex] be [tex]70.03472 cm[/tex].