A fire breaks out and increases the Kelvin temperature of a cylinder of compressed gas by a factor of 1.2. The final pressure of the gas relative to its initial pressure will be [tex]P_{2} = 1.4 P_{1}[/tex].
Given
The temperature increases by a factor of 1.2 of a compressed gas.
Or we can say that [tex]T_{2}= 1.2 T_{1}[/tex]
Where [tex]T_{1}[/tex] = Initial temperature
and [tex]T_{2}[/tex] = final temperature
we know the ideal gas equation is [tex]PV=nRT[/tex]
Where V= volume (constant) , n=constant , R=gas constant
Or P/T = constant
We can write, [tex]\frac{P_{1} }{T_{1} } =\frac{P_{2} }{T_{2} }[/tex]
[tex]P_{2}=\frac{T_{2} }{T_{1} } (P_{1} )[/tex]
So, [tex]P_{2} = 1.4 P_{1}[/tex]
Hence, the final pressure of the gas relative to its initial pressure will be [tex]P_{2} = 1.4 P_{1}[/tex].
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