Air is pumped into an automobile tyre's tube up to a pressure of `200 kPa` at `20^(@)C` As the temperature rises to `40^(@)C` the tube expand by `200%` Calculate the pressure in tube at `40^(@)C` Assume ideal nature .

Explanation

Initially `T_(1) = 293K, P_(1) = 200 xx 10^(3) Pa`
`V =V m^(3)`
Finally `T_(2) = 313k, P_(2) =P`
`V_(2) = V+ (20V)/(100) = (120V)/(100)m^(3)`
Thus `PV =nRT`
`200 xx 10^(3) xx V = nxx R xx 293`
and `P' xx (120V)/(100) =n xx R xx 313`
` p' = (313 xx 100 xx 200 xx 10^(3))/(293 xx 120)`
` =178 xx 10^(3) Pa = 178 kPa`.