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

`P_2=222.22kPa`

Step-by-step 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=(P_1V_1)/(V_2) \\ \therefore\Rightarrow \\ P_2=(P_1V_1)/(V_2) \\ P_2=((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}`