calculate the energy evolved when 8 droplets of water of radius 1/2mm each combine into one. where S=0.072N/m
To calculate the energy evolved when multiple droplets of water combine into one, we can use the concept of surface energy. Surface energy is the amount of energy required to increase the surface area of a liquid by a unit amount.
The formula for calculating surface energy is given by:
E = S * A
Where:
E = Energy evolved
S = Surface energy (given as 0.072 N/m)
A = Change in surface area
In this case, we have 8 droplets of water with a radius of 1/2 mm each. To find the change in surface area, we need to calculate the difference between the initial surface area of the individual droplets and the final surface area once they combine.
The formula to find the surface area of a sphere is:
A = 4πr^2
Where:
A = Surface area
r = Radius of the droplet
1. Calculate the initial surface area of a single droplet:
A_initial = 4π * (1/2 mm)^2
2. Calculate the final surface area of the combined droplets:
A_final = 4π * (8 * 1/2 mm)^2
3. Calculate the change in surface area:
ΔA = A_final - A_initial
4. Calculate the energy evolved using the formula:
E = S * ΔA
Plug in the values into the equation and perform the calculations. Make sure to convert the radius to meters before substituting it into the formula.
Note: Take care of unit conversions to ensure consistent units throughout the calculations.
This procedure should help you calculate the energy evolved when 8 droplets of water of radius 1/2 mm each combine into one.