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Calculate the density of a mixture formed by mixing 180 cm³ of fresh water with 2800 cm³ of sea water.

Physics

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Answer

1023.49 kg/m31023.49 \text{ kg/m}^3

Step-by-step solution

4 steps
  1. Calculate the mass of fresh water.

    Given:
    Volume of fresh water V1=180 cm3V_1 = 180 \text{ cm}^3
    Density of fresh water ρ1=1000 kg/m3\rho_1 = 1000 \text{ kg/m}^3

    First, convert the volume to cubic meters:

    V1=180 cm3=180×(10−2 m)3=180×10−6 m3V_1 = 180 \text{ cm}^3 = 180 \times (10^{-2} \text{ m})^3 = 180 \times 10^{-6} \text{ m}^3

    Now, calculate the mass of fresh water (M1=ρ1V1M_1 = \rho_1 V_1):

    M1=1000 kg/m3×180×10−6 m3M_1 = 1000 \text{ kg/m}^3 \times 180 \times 10^{-6} \text{ m}^3 M1=0.180 kgM_1 = 0.180 \text{ kg}
  2. Calculate the mass of sea water.

    Given:
    Volume of sea water V2=2800 cm3V_2 = 2800 \text{ cm}^3
    Density of sea water ρ2=1025 kg/m3\rho_2 = 1025 \text{ kg/m}^3

    First, convert the volume to cubic meters:

    V2=2800 cm3=2800×(10−2 m)3=2800×10−6 m3V_2 = 2800 \text{ cm}^3 = 2800 \times (10^{-2} \text{ m})^3 = 2800 \times 10^{-6} \text{ m}^3

    Now, calculate the mass of sea water (M2=ρ2V2M_2 = \rho_2 V_2):

    M2=1025 kg/m3×2800×10−6 m3M_2 = 1025 \text{ kg/m}^3 \times 2800 \times 10^{-6} \text{ m}^3 M2=2.870 kgM_2 = 2.870 \text{ kg}
  3. Calculate the total mass and total volume of the mixture.

    Total mass Mtotal=M1+M2M_{total} = M_1 + M_2:

    Mtotal=0.180 kg+2.870 kgM_{total} = 0.180 \text{ kg} + 2.870 \text{ kg} Mtotal=3.050 kgM_{total} = 3.050 \text{ kg}

    Total volume Vtotal=V1+V2V_{total} = V_1 + V_2:

    Vtotal=180 cm3+2800 cm3V_{total} = 180 \text{ cm}^3 + 2800 \text{ cm}^3 Vtotal=2980 cm3V_{total} = 2980 \text{ cm}^3

    Convert total volume to cubic meters:

    Vtotal=2980×10−6 m3V_{total} = 2980 \times 10^{-6} \text{ m}^3
  4. Calculate the density of the mixture.

    Density of mixture ρmix=MtotalVtotal\rho_{mix} = \frac{M_{total}}{V_{total}}:

    ρmix=3.050 kg2980×10−6 m3\rho_{mix} = \frac{3.050 \text{ kg}}{2980 \times 10^{-6} \text{ m}^3} ρmix=3.0500.002980 kg/m3\rho_{mix} = \frac{3.050}{0.002980} \text{ kg/m}^3 ρmix≈1023.49 kg/m3\rho_{mix} \approx 1023.49 \text{ kg/m}^3

    The final answer is 1023.49 kg/m3\boxed{1023.49 \text{ kg/m}^3}.


    4. Explain why fish can survive under water.

    Fish can survive underwater because they possess specialized respiratory organs called gills. Gills are highly efficient at extracting dissolved oxygen from the water. Water contains oxygen in a dissolved state, which fish absorb as it passes over their gills. The gills have a large surface area and a rich blood supply, facilitating the efficient exchange of oxygen from the water into the fish's bloodstream and carbon dioxide from the blood into the water.

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