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Problem:

The volume of an automobile engine's cylinder is $410mL$. A mixture of gasoline and air is present in it. The pressure exerted by the cylinder on the mixture is increased from $1atm$ to $9.5atm$. What will be the final volume of the mixture?

My book's solution:

Given,

Initial volume, $V_1=410mL$

Initial pressure, $P_1=1atm$

Final pressure, $P_2=9.5atm$

Final volume, $V_2=?$

Now,

$$P_1V_1=P_2V_2$$

$$[\text{Boyle's Law}]$$

$$V_2=\frac{P_1V_1}{P_2}$$

$$V_2=\frac{1\times410}{9.5}$$

$$V_2=43.157mL$$

Questions:

  1. I would've agreed with my book's solution if the mixture was completely gaseous. However, the mixture isn't completely gaseous. It has liquid elements (gasoline). Boyle's law only works for gases, right? So, is my book's process correct?
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    $\begingroup$ The gasoline is vaporized and becomes gaseous before entering the combustion chamber $\endgroup$
    – Jbag1212
    Nov 3, 2021 at 13:41

1 Answer 1

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Boyle's law assumes the temperature is constant. In an engine, the compression occurs rapidly and the energy put in as work causes an increase in temperature. Look up adiabatic compression.

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  • $\begingroup$ Given the lack of temperature data in the question, I expect that there is a hidden assumption that the temperature inside the cylinder will not increase. This is not true and because that assumption was not explicitly stated, this is obviously a poorly formulated question. $\endgroup$ Nov 3, 2021 at 17:16

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