8. (15 points) The mass of a vessel that is completely filled with kerosene is 20 kg. If this vessel is completely filled with water, its mass will be 24 kg. Determine the mass of the empty vessel. The density of water $\rho_{W}=1000 \kappa g / \mu^{3}$, the density of kerosene $\rho_{K}=800 \kappa g / \mathrm{M}^{3}$.
Answer: 4 kg

Solution. The mass of the vessel filled with kerosene: $m_{1}=m_{c}+\rho_{K} V$, where $m_{c}$ - the mass of the empty vessel, $V$ - the volume occupied by the kerosene.

The mass of the vessel filled with water $m_{2}=m_{c}+\rho_{B} V$.

(4 points)

We get that $V=\frac{m_{2}-m_{1}}{\rho_{B}-\rho_{K}}=\frac{24-20}{1000-800}=0.02 \mu^{3}$.

The mass of the empty vessel: $m_{c}=m_{1}-\rho_{\kappa} V=20-800 \cdot 0.02=4$ kg.