Solved Problem In Thermal Expansion
publicidade   

Solved Problem in Thermal Expansion
 Português     English


A square aluminum plate has an area of 2 m2 at 50 °C, if the plate is cooled to 0 °C its area decreases from 0.0044 m2. Find the coefficients of surface and linear expansion of aluminum

Problem data
Problem diagram

Aluminum plate with 2 square meters of area at 50 degrees Celsius, under a decrease in temperature to 0 degrees Celsius its area decreases from 0.0044 square meters.
figure 1

As the plate decreases, upon cooling, the signal of the surface area change is negative.

Solution

Writing the equation of area thermal expansion, we have
\[ \bbox[#99CCFF,10px] {\Delta A=\beta A_{0}\Delta t} \]
\[ \Delta A=\beta A_{0}(\;t_{\text{f}}-t_{\text{i}}\;)\\ -0.0044=\beta \times 2 \times (\;0-50\;)\\ -0,0044=-100\beta \\ \beta =\frac{-0.0044}{-100}\\ \beta =\frac{4.4 \times 10^{-3}}{1 \times 10^{2}}\\ \beta =4.4 \times 10^{-3} \times 10^{-2}\\ \beta =4.4 \times 10^{-5}\\ \beta=0.000044 \]
\[ \bbox[#FFCCCC,10px] {\beta =4.4 \times 10^{-5} °{\text{C}}^{-1}} \]
The coefficient of linear thermal expansion of aluminum
\[ \bbox[#99CCFF,10px] {\beta =2\alpha } \]
\[ \alpha=\frac{\beta }{2}\\ \alpha=\frac{4.4 \times 10^{-5}}{2} \]
\[ \bbox[#FFCCCC,10px] {\alpha =2.2 \times 10^{-5} °{\text{C}}^{-1}} \]

publicidade