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A gas cyclinder containing cooking gas c...

A gas cyclinder containing cooking gas can withstand a pressure of `14.9 atm`. The pressure gauge of cyclinder indicates `12 atm` at `27^(@) C`. Due to sudden fire in building the temperature starts rising. The temperature at which the cyclinder will explode is

Text Solution

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From the available data : `P_(1) = 14.9 ` bar , `T_(1) = ?`
`P_(2) = 12.0` bar , `T_(2) = 27 + 273 = 300 K`
Since the gas is kept in the cylinder, its volume remains constant. According to Gay-Lussac's law.
`(P_(1))/(P_(2)) = (T_(1))/(T_(2))` or `T_(1) = (P_(1))/(P_(2)) xx T_(2) , T_(1) = ((14.9 "bar") xx (300 K))/((12 "bar")) = 372.5 K`
`:.` Cylinder will explode at a temperature `= 372.5 - 273 = 99.5^(@)C`.
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