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.
A
80
B
257
C
255
D
256
Text Solution
Verified by Experts
The correct Answer is:
c
(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
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