Certainly! Let's solve the problem step-by-step.
1. Identify the initial conditions and constants:
- Initial volume ([tex]\( V_i \)[/tex]): 2.00 m³
- Initial temperature ([tex]\( T_i \)[/tex]): 22.5°C
- Final temperature ([tex]\( T_f \)[/tex]): 627°C
2. Determine the coefficient of volume expansion for concrete:
- From the class textbook, the coefficient of volume expansion ([tex]\( \beta \)[/tex]) is [tex]\( 3.6 \times 10^{-5} \)[/tex] [tex]\( \text{°C}^{-1} \)[/tex].
3. Calculate the change in temperature:
[tex]\[
\Delta T = T_f - T_i = 627^\circ\text{C} - 22.5^\circ\text{C} = 604.5^\circ\text{C}
\][/tex]
4. Calculate the increase in volume ([tex]\( \Delta V \)[/tex]):
[tex]\[
\Delta V = V_i \times \beta \times \Delta T
\][/tex]
Plugging in the values:
[tex]\[
\Delta V = 2.00 \, \text{m}^3 \times 3.6 \times 10^{-5} \, \text{°C}^{-1} \times 604.5\,^\circ\text{C}
\][/tex]
5. Perform the multiplication to find the increase in volume:
[tex]\[
\Delta V = 2.00 \times 3.6 \times 10^{-5} \times 604.5
\][/tex]
[tex]\[
\Delta V = 0.043536
\][/tex]
6. Round the answer to 3 significant digits:
[tex]\[
\Delta V \approx 0.044
\][/tex]
So, the volume of the concrete block will increase by approximately 0.044 m³.
