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a fire breaks out and increases the Kelvin temperature of a cylinder of compressed gas by a factor of 1.2 What is the final pressure of the gas relative of a initial pressure

Answer :

According to the Gay-Lussac's Law, if an ideal gas is at constant volume, then the quotient of its pressure and its temperature is also constant:

[tex]\frac{P_1}{T_1}=\frac{P_2}{T_2}[/tex]

If the final temperature is 1.2 times the initial temperature, then, substitute T_2=1.2*T_1 and solve for P_2:

[tex]\begin{gathered} T_2=1.2T_1 \\ \Rightarrow\frac{P_1}{T_1}=\frac{P_2}{1.2T_1} \\ \Rightarrow P_2=\frac{P_1}{T_1}\times1.2T_1 \\ \Rightarrow P_2=1.2P_1 \end{gathered}[/tex]

Therefore, the final pressure of the gas is 1.2 times the initial pressure.

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