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Gay-Lussac's LawIt states that: "At constant volume the pressure of a gas sample is directly proportional to the absolute temperature."This means that doubling the pressure of the gas will cause its absolute temperature to double.Mathematically this law is expressed as: [tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\dfrac{P_{1}}{T_{1}}=\frac{P_{2}}{T_2} \iff \ P_1T_2=P_2T1 } \end{gathered}$} }[/tex]We have that the data is:P₁ = 0.87 atmT₁ = 25 °C + 273 = 298 KT₂ = 50 °C + 273 = 323 KP₂ = ?We clear for the final pressure:[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{P_{2}=\frac{P_1T_2}{T_{1}} } \end{gathered}$}}[/tex][tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{P_{2}=\frac{(0.87 \ atm)\cdot(323\not{k})}{298\not{k}} } \end{gathered}$}}[/tex][tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{P_{2}=0.94 \ atm } \end{gathered}$}}}[/tex]If the temperature increases to 50°C, its new pressure will be 0.94 atm.
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