A gas cylinder withstand a pressure of 14.9 atm

Asked by admin @ 23/08/2021 in Chemistry viewed by 306 People

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

Answered by admin @ 23/08/2021

From the given,

${ P }_{ 1 }$ = 12 bar

${ T }_{ 1 }$ = 27°C + 273 = 300 K

${ P }_{ 2 }$ = 14.9 bar

${ T }_{ 1 }$ = ?

According to the pressure temperature law,

$\frac { { P }_{ 1 } }{ { P }_{ 2 } } \quad =\quad \frac { { T }_{ 1 } }{ { T }_{ 2 } } \\\\ { T }_{ 2 }\quad =\quad \frac { { T }_{ 1 }\quad \times \quad { P }_{ 2 } }{ { P }_{ 1 } }$

Substituting the given values,

${ T }_{ 2 }\quad =\quad \frac { 300\quad \times \quad 14.9 }{ 12 } \\\\ =\quad 372.5\quad K$

Temperature in centigrade = 372.5 - 273 = 99.5°C

Therefore, the cylinder will be at 99.5°C.

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