Question

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 1

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:

`(P_1)/(T_1)=(P_2)/(T_2)`

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

`\begin{gathered} T_2=1.2T_1 \\ \Rightarrow(P_1)/(T_1)=(P_2)/(1.2T_1) \\ \Rightarrow P_2=(P_1)/(T_1)*1.2T_1 \\ \Rightarrow P_2=1.2P_1 \end{gathered}`

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