A cylindrical brass container with a base of 80.0 cm^2 and height of 20.0 cm is filled to the brim with water when the system is at 25.0° C. How much water overflows when the temperature of the water and the container is raised to 96.1° C? (The coefficient of volume expansion for water and brass are 2.07x10^-4 K^1 and 5.7x10^-5 K^−1, respectively.)

Question

A cylindrical brass container with a base of 80.0 cm^2 and height of 20.0 cm is filled to the brim with water when the system is at 25.0° C. How much water overflows when the temperature of the water and the container is raised to 96.1° C? (The coefficient of volume expansion for water and brass are 2.07x10^-4 K^1 and 5.7x10^-5 K^−1, respectively.)
cm3

Please someone help out I don't know how to do this. Thank you.

Elena · Answer

Volume of water at 25° C = 80 • 20 = 1600 cm^3.
Volume of water at 96.1° C = 1600 • [1 + 2.07 •10^-4 (96.1 - 25)] cm^3.
Volume of brass container at 96.1° C = 1600 • [1 + 5.7•10^-5 (96.1 - 25)] cm^3
=> volume of overflown water (subtracting the above two volumes)
= 1600 • [(20.7 - 5.7) •10^-5] • (96.1 - 25) cm^3 = 17.064 cm^3