If the pressure exerted on a confined gas is doubled, what happens to the volume of the gas?

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Answer 1 · 2016-10-27T06:46:57

$Boyle's Law$ $"Boyle's Law"$ holds that at constant,,,,,,,,,,,,

$Boyle's Law$ $"Boyle's Law"$ holds that at constant temperature, and constant amount of gas, pressure is inversely proportional to volume:

$P \propto \frac{1}{V}$ $Pprop1/V$ , or $P_{1} V_{1} = P_{2} V_{2}$ $P_1V_1=P_2V_2$ .

And thus $V_{2}$ $V_2$ $=$ $=$ $\frac{P_{1} V_{1}}{P_{2}}$ $(P_1V_1)/P_2$

But the boundary conditions of the problem state that $P_{2} = 2 P_{1}$ $P_2=2P_1$ :

Thus $V_{2}$ $V_2$ $=$ $=$ $(cancel(P_1)V_1)/(2cancel(P_1))$

So $V_2=V_1/2$

So the volume is HALVED.