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.
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
To find out how much water overflows when the temperature is raised from 25.0°C to 96.1°C, we need to determine the change in volume of both the brass container and the water.
First, let's calculate the change in volume for the cylindrical brass container:
The formula for the volume of a cylinder is V = base area * height.
Given that the base area is 80.0 cm^2 and the height is 20.0 cm, we can calculate the initial volume of the brass container as follows:
V_initial = 80.0 cm^2 * 20.0 cm = 1600 cm^3
Now we need to calculate the change in volume of the brass container due to the change in temperature. The formula for the change in volume of an object due to a change in temperature is ΔV = V_initial * β * ΔT, where β is the coefficient of volume expansion and ΔT is the change in temperature.
Given that the coefficient of volume expansion for brass is 5.7x10^-5 K^−1 and the change in temperature is ΔT = 96.1°C - 25.0°C = 71.1°C, we can calculate the change in volume of the brass container as follows:
ΔV_brass = V_initial * β * ΔT
= 1600 cm^3 * (5.7x10^-5 K^−1) * 71.1°C
Now let's calculate the change in volume for the water in the brass container:
Similar to the brass container, we use the formula V_water = base area * height to calculate the initial volume of water in the container:
V_water_initial = 80.0 cm^2 * 20.0 cm = 1600 cm^3
The change in volume of water is calculated using the same formula for the change in volume of an object due to a change in temperature:
ΔV_water = V_water_initial * β * ΔT
= 1600 cm^3 * (2.07x10^-4 K^1) * 71.1°C
Finally, we need to determine how much water overflows when the temperature is raised. This can be calculated by subtracting the change in volume of the brass container from the change in volume of water:
ΔV_overflow = ΔV_water - ΔV_brass
Now you can substitute the values in the above equations, perform the calculations, and find out how much water overflows when the temperature is raised to 96.1°C.