Question

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?

Answer 1

Answer:

0.0014352 inch

Explanation:

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

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

$d_0$ = Original diameter = 8 in

$\Delta T$ = Change in temperature

Change in diameter of steel

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

Change in diameter of copper

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

Difference in diameter is given by

$\Delta d=\Delta d_s-\Delta d_c\\\Rightarrow \Delta d=0.0827632-0.081328\\\Rightarrow d=0.0014352\ in$

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