Question

An ideal gas is confined within a closed cylinder at atmospheric pressure (1.013 * 105 Pa) by a piston. The piston moves until the volume of the gas is reduced to one-ninth of the initial volume. What is the final pressure of the gas when its temperature returns to its initial value?

Answer 1

Answer:

$911700\ \text{Pa}$

Explanation:

$P_1$ = Initial pressure = $1.013\times 10^5\ \text{Pa}$

$V_1$ = Initial volume

$V_2$= Final volume = $\dfrac{V_1}{9}\\\Rightarrow \dfrac{V_1}{V_2}=9$

Temperature is the same in the initial and final state

From the ideal gas law we have

$P_1V_1=P_2V_2\\\Rightarrow P_2=\dfrac{P_1V_1}{V_2}\\\Rightarrow P_2=P_1\times9\\\Rightarrow P_2=1.013\times 10^5\times 9\\\Rightarrow P_2=911700\ \text{Pa}$

The final pressure of the system is $911700\ \text{Pa}$.