A gas cylinder containing cooking gas can withstand a pressure of 14.9 bar. The pressure gauge of the cylinder indicates 12 bar at 27°C. Due to sudden fire in the building, the temperature starts rising. At what temperature will the cylinder explode?

Solution

Since the gas is confirmed in a cylinder, its volume will remain constant.
From the given data,
$straight P subscript 1 space equals space 12 space bar semicolon space space space space space straight T subscript 1 space equals space 27 plus 273 space equals space 300 space straight K straight P subscript 2 space equals space 14.9 space bar semicolon space space space straight T subscript 2 space equals space ?$
Applying pressure temperature law,
$straight P subscript 1 over straight P subscript 2 space equals space straight T subscript 1 over straight T subscript 2$
$or space space space space straight T subscript 2 space equals space fraction numerator straight T subscript 1 space cross times space straight P subscript 2 over denominator straight P subscript 1 end fraction$
Substituting the values in the above equation,
$straight T subscript 2 space equals space fraction numerator 300 space cross times space 14.9 over denominator 12 end fraction space equals space 372.5 space straight K$
$Temperature space in space degree straight C space equals space 372.5 space minus space 273 space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 99.5 space degree straight C space space space space space$
Hence the cylinder will at $99.5 space degree straight C.$