A balloon containing 1 mole air at 1 atm initially is filled further with air till pressure increases to 4 atm. The intial diameter of the ballon is 1 m and the pressure at each stage is proportional to diameter of the balloon. How many moles of air added to change the pressure from 1 atm to 4 atm.

Options

A. 80
B. 257
C. 255
D. 256

Answer

c

Explanation

(c) `P prop d, p=kd and k=(1 "atm")/(1 "metre")`
`PV=nRT, kd((1)/(6)pid^(3))=nRT,`
`(d_(1)^(4))/(d_(2)^(4))=(n_(1))/(n_(2)),(1)/(4^(4))=n_(1)//n_(2),n_(2)=256`
no. of moles added=256 - 1 =255