Which of the following correctly gives the mass density and the weight density of water at 4°C?

• A. Mass density: 0.997 g/cm^3; Weight density: 1.00 kN/m^3
• B. Mass density: 1.00 g/cm^3; Weight density: 9.81 kN/m^3
• C. Mass density: 1.00 kg/m^3; Weight density: 9.81 N/m^3
• D. Mass density: 9.81 g/cm^3; Weight density: 1.00 kN/m^3

Answer: (B)

Verified step by step guidance

1. Understand the definitions: Mass density (\rho) is the mass per unit volume, typically expressed in units like g/cm^3 or kg/m^3. Weight density (\gamma) is the weight per unit volume, which is the force due to gravity on the mass per unit volume, expressed in units like N/m^3 or kN/m^3.
2. Recall the known value for the mass density of water at 4°C, which is approximately 1.00 g/cm^3 or equivalently 1000 kg/m^3. This is a standard reference value in chemistry and physics.
3. Calculate the weight density using the formula: \(\gamma = \rho \times g\) where \(\rho\) is the mass density in kg/m^3 and \(g\) is the acceleration due to gravity (approximately 9.81 m/s^2).
4. Convert units carefully: Since mass density is often given in g/cm^3, convert it to kg/m^3 by multiplying by 1000 (because 1 g/cm^3 = 1000 kg/m^3). Then multiply by 9.81 m/s^2 to get weight density in N/m^3. To express weight density in kN/m^3, divide the result by 1000.
5. Compare the calculated values with the options given to identify the correct pair of mass density and weight density for water at 4°C.