Question

calculate the energy spent on spraying a drop of mercury of 1 cm radius into 10^6 droplets all of same radius. surface tension of mercury is 0.035N/m

Answer 1

ANS : .Energy spent on spraying =
`4.3542*10^(-4)J`

Step-by-step explanation:

Given:

• Radius of mercury = 1cm initially ;
• split into
  `10^(6)` drops ;

Thus, volume is conserved.

i.e ,

`(4)/(3) \pi R_(o)^(3) = 10^(6)*(4)/(3) \pi R_(n)^(3)\\R_(n)=(R_(o))/(10^(2)) = (1cm)/(100) = 0.01 cm`

• Energy of a droplet =
  `T`Δ
  `A`

Where ,

• T is the surface tension
• ΔA is the change in area

Initial energy
`E_(i) = T*A_(i)\\= 0.0035 * 4 *\pi *0.01^(2)\\=4.398*10^(-6)J`

Final energy
`E_(f)=10^(6)*T*A_(f)\\=10^(6)*0.0035*4*\pi *(0.0001)^2\\=4.39823*10^(-4)`

∴ .Energy spent on spraying =
`=E_(f)-E{i}\\=(439.823-4.39823)*10^(-6)\\=4.3542*10^(-4)J`

ANS : .Energy spent on spraying =
`4.3542*10^(-4)J`