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The Ideal Gas Equation

An ideal gas ...

Question

An ideal gas undergoes an state change according to $P V$ diagram. What is the value of $V_{x}$ ?

\frac{V_{0}}{2}

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V_{0}

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2 V_{0}

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\frac{V_{0}}{4}

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Solution

The correct option is A $\frac{V_{0}}{2}$
Boyle's law:
The absolute pressure exerted by a given mass of an ideal gas is inversely proportional to the volume it occupies if the temperature and amount of gas remain unchanged within a closed system.
$P_{1} V_{1} = P_{2} V_{2}$

Initial,
$P_{1} = P_{0}$
$V_{1} = V_{0}$
Final,
$P_{2} = 2 P_{0}$
$V_{2} = V_{x}$

$P_{1} V_{1} = P_{2} V_{2}$
$\Rightarrow P_{0} V_{0} = 2 P_{0} V_{x} \Rightarrow V_{x} = \frac{V_{0}}{2}$ .
Option A is correct.

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