Answer to Question #287221 in Physics for Haruto

Question

The density of air at standard conditions (p = 1 atm and t = 20°c) is 1.28 kg/m³. At what pressure is the density 0.64 kg/m³ if the temperature and number of molecules are kept constant?

Answer 1

$$\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2},\\\space\\ \dfrac{P_1(m/\rho_1)}{T}=\dfrac{P_2(m/\rho_2)}{T},\\\space\\ \dfrac{P_1}{\rho_1}=\dfrac{P_2}{\rho_2},\\\space\\ P_2=\rho _2P_1/\rho_1=0.5\text{ atm}.$$