A ballon blown up with 1 mole of gas has a volume of `480mL` at `5^(@)C` The balloon is filled to (7/8) th of its maximum capacity Suggest
(a) Will the balloon burst at `30^(@)C`
(b) The minimum temperature at which it will burst
(c ) The pressure of gas inside the balloon at `5^(@)C`
(d) The pressure of gas when balloon bursts .

Explanation

Maximum capacity or volume of balloon
` =(8)/(7) xx 480 = 548 .47 mL`
Also `V_(1) = 480 mL, T_(1) = 278K, n =1` mole
(a) The ballon will burst at the temperature say `T_(2)` when volume becomes `548.57 mL`
`:' (V_(1))/(T_(1)) = (V_(2))/(T_(2))`
`(480)/(278) = (548.57)/(T_(2))`
`T_(2) = 317.71K =44.71^(@)C`
Thus ballon will not burst at `30^(@)C`
(b) The minimum temperature at which ballon dursts is `44.71^(@)C`
(c ) Pressure of gas at `5^(@)C` having 1 mole and
`V =480mL`
`P xx (480)/(1000) =1 xx 0.0821 xx 278`
`P =47.5atm`
(d) Since `V` increases with temperature rise from `5^(@)C` to `44.71^(@)C` at which ballon bursts and therefore pressure remains constant Thus pressure of gas in ballon when it bursts in `47.5 atm` .