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A cylinderical of cooking gas can withst...

A cylinderical of cooking gas can withstand a pressure of 14.9 atm at `27^(@)C`, the pressure gauge of the cylinder records a pressure of 12 atm. Due to a sudden fire in the building, the temperature starts rising. At what temperature, will the cylinder explode?

Text Solution

Verified by Experts

We know, `(P_(1))/(P_(2))=(T_(1))/(T_(2))`
The cylinder can withstand pressure of 14.9 atm
If the pressure of the cylinder at `T_(2)K` is 14.9 atm,
then `T_(2)=(P_(2))/(P_(1))xxT_(1)=(14.9)/(12)xx300=372.5K`
`[because P_(1)=12" atm and "T_(1)=(273+27)=300K]`
As the cylinder can withstand pressure upto 14.9 atm, it will explode at a pressure above 14.9 atm. the pressure of the cylinder becomes greater than 14.9 atm when the temperature is greater than 372.5 K or `99.5^(@)C`. hence the cylinder will explode at a temperature greater than `99.5^(@)C`.
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