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What happens when the volume of a fixed mass of gas is doubled?

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Last updated date: 16th Jul 2024
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Answer
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Hint :We know that Use the equation of ideal gas law. Use Boyle’s law equation to find the relation between pressure and volume. Apply the given conditions to the ideal gas law equation and find what happens to the n value.

Complete Step By Step Answer:
We know the ideal gas law is obtained from Boyle's law. Boyle’s Law states that for a fixed mass of gas at a constant temperature, the volume of the gas is inversely proportional to the pressure of the gas.
We can use the Ideal Gas Equation to solve this question: $ PV=nRT $
 $ P $ is pressure in $ Pa $
 $ V $ is volume in $ {{m}^{3}} $
 $ n $ is number of moles of gas
 $ R $ is the universal gas constant, $ 8.31\text{ }J/K\text{ }mol $
 $ T $ is temperature in Kelvin
In your scenario, when mass is fixed, the number of moles will be fixed, too. So we can combine both constant terms n and R to give us: $ PV=kT $ where k is a constant.
Now, since we want to work out how volume changes, let's put V on the left-hand side and move P to the right-hand side: $ V=\dfrac{kT}{P} $
So from the equation, we can deduce that when temperature and pressure are both doubled, the Volume $ V~ $ will remain unchanged as the numerator term $ T $ and the denominator term $ P $ are both affected by a multiple of $ 2, $ hence can be cancelled away: $ V=\dfrac{kT\left( \times 2 \right)}{P\left( \times 2 \right)}=\dfrac{kT}{P} $
Therefore, when the volume of a fixed mass of gas is doubled the pressure is inversely proportional to volume. Thus, when volume is doubled, the pressure is halved.

Note :
Remember that the given question can also be solved by considering Charles' law, which states that for a fixed mass at constant pressure on the gas, the volume of the gas is directly proportional to the temperature of the gas.