Contraction · Estonian PhO 2018 #1

Physics

Problem

V_w

liters of water and

V_e

liters of ethanol are mixed with each other so that the volume of their solution is

V=\SI{1}{dm^3}

and that by mass there is

p=\SI{44,1}{\percent}

of ethanol in the solution. Find the volumes

V_w

and

V_e

of the water and ethanol mixed with each other. When pouring the solutions together there is a

\gamma = \SI{6}{\percent}

of contraction – the volume of the acquired solution is 6\% smaller than the total volume of water and ethanol. The density of water is

\rho_w=\SI{1000}{kg/m^3}

and ethanol

\rho_e=\SI{790}{kg/m^3}