# If I have 5.6 liters of gas in a piston at a pressure of 1.5 atm and compress the gas until its volume is 4.8 L, what will the new pressure inside the piston be?

Feb 24, 2017

${P}_{2} = 1.75 \cdot a t m \ldots \ldots \ldots$

#### Explanation:

At constant $T$, ${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$.......

We solve for ${P}_{2} = \frac{{P}_{1} {V}_{1}}{V} _ 2$, and clearly the $\text{RHS}$ will have the required units of pressure:

${P}_{2} = \frac{1.5 \cdot a t m \times 5.6 \cdot L}{4.8 \cdot L} = 1.75 \cdot a t m$

That ${P}_{2} > {P}_{1}$ is quite reasonable, because we are compressing the piston.