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The volume V of an ideal gas varies directly with the temperature T and inversely with the pressure P. A cylinder contains oxygen at a temperature of 310 degrees K and a pressure of 18 atmospheres in a volume of 120 liters. Find the pressure if the volume is decreased to 100 liters and the temperature is increased to 350 degrees K. Round your answer to two decimal places. The pressure is Number atmospheres.



Answer :

[tex]\begin{gathered} V\propto T \\ V\propto\frac{1}{P} \end{gathered}[/tex]

Therefore:

[tex]\begin{gathered} V=k\frac{T}{P} \\ \end{gathered}[/tex]

Where:

k = Constant of proportionality

T = Temperature

V = Volume

P = Pressure

A cylinder contains oxygen at a temperature of 310 degrees K and a pressure of 18 atmospheres in a volume of 120 liters. So:

[tex]\begin{gathered} T=310 \\ P=18 \\ V=120 \\ so\colon \\ 120=k\frac{310}{18} \\ solve_{\text{ }}for_{\text{ }}k \\ k=\frac{120\cdot18}{310} \\ k\approx6.9677 \end{gathered}[/tex]

Therefore, if the volume is decreased to 100 liters and the temperature is increased to 350 degrees K. The pressure will be:

[tex]\begin{gathered} P=k\frac{T}{V} \\ P=6.9677\cdot\frac{350}{100} \\ P\approx24.39 \end{gathered}[/tex]

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