Hello!
If I initially have a gas at a pressure of 12 atm, volume of 23 liters, and temperature of 200 K, and then I raise the pressure to 14 atm and increase the temperature to 300 K, what is the new volume of the gas?
We have the following data:
P1 (initial pressure) = 12 atm
V1 (initial volume) = 23 L
T1 (initial temperature) = 200 K
P2 (final pressure) = 14 atm
T2 (final temperature) = 300 K
V2 (final volume) = ? (in L)
Now, we apply the data of the variables above to the General Equation of Gases, let's see:
[tex]\dfrac{P_1*V_1}{T_1} =\dfrac{P_2*V_2}{T_2}[/tex]
[tex]\dfrac{12*23}{200} =\dfrac{14*V_2}{300}[/tex]
[tex]\dfrac{276}{200} =\dfrac{14\:V_2}{300}[/tex]
multiply the means by the extremes
[tex]200*14\:V_2 = 276*300[/tex]
[tex]2800\:V_2 = 82800[/tex]
[tex]V_2 = \dfrac{82800\!\!\!\!\!\!\!\dfrac{\hspace{0.4cm}}{~}}{2800\!\!\!\!\!\!\!\dfrac{\hspace{0.4cm}}{~}}[/tex]
[tex]V_2 \approx 29.57142857... \to \boxed{\boxed{V_2 \approx 30\:L}}\:\:\:\:\:\:\bf\blue{\checkmark}[/tex]
*** Note: the approximation rule says that when the number before the digit 5 is odd, the previous value is raised to the next even number
Answer:
The new volume is approximately 30 Liters
_______________________
[tex]\bf\green{I\:Hope\:this\:helps,\:greetings ...\:Dexteright02!}\:\:\ddot{\smile}[/tex]
