Hi, I was working through a past exam paper when I came across a Boyle's Law question in which the answer to the second part confused me. I will write the question, part one and its solution and the second part. Here is the question :(adsbygoogle = window.adsbygoogle || []).push({});

A rigid cylinder contains [tex]0.08 m^3[/tex] of helium gas at a pressure of 750 kPa. Gas is released from the cylinder to fill party balloons. During the filling process, the temperature remains constant. When filled, each balloon holds [tex]0.020 m^3[/tex] of helium gas at a pressure of 125 kPa.

(a) Calculate the total volume of the helium gas when it is at a pressure of 125 kPa.

Solution :

Using [tex]P_{1}V_{1} = P_{2}V_{2}[/tex]

[tex](7.5*10^5)(0.08) = (1.25*10^5)V_{2}[/tex]

[tex]V_{2} = 0.48 m^3[/tex]

(b) Determine the maximum number of balloons which can be fully inflated by releasing gas from the cylinder.

My answer to this question was as follows :

[tex]Number of balloons = \frac{V_{2}}{0.020} = \frac{0.48}{0.020} = 24 balloons[/tex]

But when I looked at the answer sheet this is what was written:

[tex]Volume of gas available = 0.48 - 0.08 = 0.40 m^3[/tex]

[tex]Number of balloons = \frac{0.40}{0.020} = 20 balloons[/tex]

My confusion is in the part where the volume of 0.08 cubic metres is taken off the total volume obtained from a pressure of 125 kPa. I know that the 0.08 is the same volume in the cylinder but why is this taken away from it, if the pressure is changed isn't the gas the new volume of 0.48 cubic metres?

I would really appreciate any helpful advice given, thank you in advance.

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# Homework Help: Boyle's Law Question

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