Question

A syringe is filled with air of volume 10 cm at 100 kPa and then sealed. Itis compressed so that its volume is reduced by 45 %. Find the pressureinside it.

Answer 1

Answer:

$P_2=222.22kPa$

Explanation: By using Gas Law, the new pressure can be calculated as follows:

Gas law states:

$(P_1V_1=P_2V_2)\Rightarrow(1)$

Using (1), and Identifying the knowns and unknowns, and plugging in (1) we get the following results:

$\begin{gathered} V_1=10cm^3=1\cdot10^{-5}m^3 \\ P_1=100\text{kPa}=100000Pa \\ V_2=(0.45)\cdot V_1=(0.45)\cdot(1\cdot10^{-5}m^3)=4.5\cdot10^{-6}m^3 \\ V_2=4.5\cdot10^{-6}m^3 \end{gathered}$

Finally, the New pressure is calculated as follows:

$\begin{gathered} (P_1V_1=P_2V_2)\Rightarrow(1) \\ P_2=\frac{P_1V_1}{V_2} \\ \therefore\Rightarrow \\ P_2=\frac{P_1V_1}{V_2} \\ P_2=\frac{(100000Pa)\cdot(1\cdot10^{-5}m^3)}{(4.5\cdot10^{-6}m^3)} \\ P_2=2.22\cdot10^5Pa \\ P_2=222.22kPa \end{gathered}$