Given parameters:
Initial volume = 120ml
Initial temperature = 35°C
Initial pressure = 1.2bar
Final volume = 180ml
Final temperature = 35°C
Unknown:
Final pressure = ?
To solve this problem, we apply the combined gas law. The expression is given below;
[tex]\frac{P_{1}V_{1} }{T_{1} } = \frac{P_{2}V_{2} }{T_{2} }[/tex]
Where P₁ is the initial pressure
P₂ is the final pressure
V₁ is the initial volume
V₂ is the final volume
T₁ is the initial temperature
T₂ is the final temperature
We need to convert the parameters to standard units
take the volume to dm³;
1000ml = 1dm³
120ml = [tex]\frac{120}{1000}[/tex] dm³ = 0.12dm³ = initial volume
Final volume;
1000ml = 1dm³
180ml = [tex]\frac{180}{1000}[/tex] dm³ = 0.18dm³
Now, the temperature;
K = 273 + °C
Initial temperature = 273 + 35 = 308k
Final temperature = 308k
We then input the parameters into the equation;
[tex]\frac{1.2bar x 0.12 }{308} = \frac{P_{2} x 0.18 }{308}[/tex]
Solving for P₂;
P₂ = 0.8bar
The new pressure or final pressure in the vessel is 0.8bar
