Answer:
[tex]p_2 = 664081 N/m^{2}[/tex]
Explanation:
from the ideal gas law we have
PV = mRT
[tex]P = \rho RT[/tex]
[tex]\rho = \frac{P}{RT}[/tex]
HERE R is gas constant for dry air = 287 J K^{-1} kg^{-1}
[tex]\rho = \frac{7.00 10^{5}}{287(18+273)}[/tex]
[tex]\rho = 8.38 kg/m^{3}[/tex]
We know by ideal gas law
[tex]\rho = \frac{m_1}{V_1}[/tex]
[tex]m_1 = \rho V_1 = 8.38 *2*10^{-3}[/tex]
[tex]m_1 = 0.0167 kg[/tex]
for m_2
[tex]m_2 = \rho V_i - V_removed[/tex]
[tex]m_2 = 8.38*(.002 - 10^{-4})[/tex]
[tex]m_2 = 0.0159 kg[/tex]
WE KNOW
PV = mRT
V, R and T are constant therefore we have
P is directly proportional to mass
[tex]\frac{p_2}{p_1}=\frac{m_2}{m_1}[/tex]
[tex]p_2 = p_1 * \frac{m_2}{m_1}[/tex]
[tex]p_2 =7*10^{5} * \frac {.0159}{0.0167}[/tex]
[tex]p_2 = 664081 N/m^{2}[/tex]
