According to Boyle's Law, an ideal gas at a constant temperature will satisfy the following relation between the initial and final conditions of pressure and volume:
[tex]P_1V_1=P_2V_2[/tex]Isolate P_2 from the equation:
[tex]P_2=\frac{_{}P_1V_1_{}_{}}{V_2}[/tex]Substitute the values for the initial pressure as well as for the two volumes to find the value of the final pressure of the gas:
[tex]\begin{gathered} P_2=\frac{(200Pa)(0.500m^3)}{(0.150m^3)} \\ =667Pa \end{gathered}[/tex]Therefore, the final pressure of the gas is:
[tex]667Pa[/tex]