Question #78718
A metal sheet of area 100cm^2 was heated through 70K. Calculate its new area if the linear expansivity of the metal is 0.000017K^-1
Expert's answer
By the definition of the area thermal expansion we have:
∆A/A_0 =2α∆T,
here, ∆A is the change in the area of the metal sheet after the change in temperature, A_0 is the area of the metal sheet before the change in temperature, α is the coefficient of linear expansion for the metal, and ∆T is the change in temperature.
Then, from this formula we can find the change in the area of the metal sheet:
∆A=2αA_0 ∆T=2∙1.7∙〖10〗^(-5) K^(-1)∙100 cm^2∙70 K=0.24 cm^2.
Finally, we can find the new area of the metal sheet:
A=A_0+∆A=100 cm^2+0.24 cm^2=100.24 cm^2.
∆A/A_0 =2α∆T,
here, ∆A is the change in the area of the metal sheet after the change in temperature, A_0 is the area of the metal sheet before the change in temperature, α is the coefficient of linear expansion for the metal, and ∆T is the change in temperature.
Then, from this formula we can find the change in the area of the metal sheet:
∆A=2αA_0 ∆T=2∙1.7∙〖10〗^(-5) K^(-1)∙100 cm^2∙70 K=0.24 cm^2.
Finally, we can find the new area of the metal sheet:
A=A_0+∆A=100 cm^2+0.24 cm^2=100.24 cm^2.
