Respuesta :
Answer:
The volume of an aluminum cube is 0.212 cm³.
Explanation:
Given that,
Edge of cube = 4.00 cm
Initial temperature = 19.0°C
Final temperature = 67.0°C
linear expansion coefficient [tex]\alpha=23.0\times10^{-6}/C^{\circ}[/tex]
We need to calculate the volume expansion coefficient
Using formula of volume expansion coefficient
[tex]\beta=3\alpha[/tex]
Put the value into the formula
[tex]\beta=3\times23.0\times10^{-6}[/tex]
[tex]\beta=0.000069=69\times10^{-6}/C^{\circ}[/tex]
We need to calculate the volume
[tex]V= a^3[/tex]
[tex]V=4^3[/tex]
[tex]V=64\ cm^3[/tex]
The change temperature of the cube is
[tex]\Delta T=T_{f}-T_{i}[/tex]
Put the value into the formula
[tex]\Delta T=67-19 = 48^{\circ}C[/tex]
We need to calculate the increases volume
Using formula of increases volume
[tex]\Delta V=V\beta\Delta T[/tex]
Put the value into the formula
[tex]\Delta V=64\times69\times10^{-6}\times48[/tex]
[tex]\Delta V=0.212\ cm^3[/tex]
Hence, The volume of an aluminum cube is 0.212 cm³.
