Some cookware has a stainless steel interior (α=17.3×10−6K−1) and a copper bottom (α=17.0×10−6K−1) for better heat distribution. Suppose an 8.0-in. pot of this construction is heated to 620 ∘C on the stove. Part A If the initial temperature of the pot is 22 ∘C, what is the difference in diameter change for the copper and the steel?

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boffeemadrid boffeemadrid · Answer 1 · 2019-12-11T08:17:45+01:00

Answer:

0.0014352 inch

Explanation:

[tex]\alpha_s[/tex] = Coefficient of linear expansion of steel = [tex]17.3\times 10^{-6}\ /K[/tex]

[tex]\alpha_c[/tex] = Coefficient of linear expansion of copper = [tex]17\times 10^{-6}\ /K[/tex]

[tex]d_0[/tex] = Original diameter = 8 in

[tex]\Delta T[/tex] = Change in temperature

Change in diameter of steel

[tex]\Delta d_s=\alpha_sd_0\Delta T\\\Rightarrow \Delta d_s=17.3\times 10^{-6}\times 8\times (620-22)\\\Rightarrow \Delta d_s=0.0827632\ in[/tex]

Change in diameter of copper

[tex]\Delta d_c=\alpha_sd_0\Delta T\\\Rightarrow \Delta d_c=17\times 10^{-6}\times 8\times (620-22)\\\Rightarrow \Delta d_c=0.081328\ in[/tex]

Difference in diameter is given by

[tex]\Delta d=\Delta d_s-\Delta d_c\\\Rightarrow \Delta d=0.0827632-0.081328\\\Rightarrow d=0.0014352\ in[/tex]

The difference in diameter change for the copper and the steel is 0.0014352 inch