Final answer:
The work done by the pump is calculated using the mass of the oil, the acceleration due to gravity, and the height the oil is lifted to, resulting in 110,452.5 J.
Step-by-step explanation:
To calculate the work done by the pump in delivering 0.550 m³ of oil to a height of 25.0 m, we'll consider the density of the oil and the force due to gravity. First, we convert the density of oil from g/cm³ to kg/m³ by multiplying by 1000 (since 1 g/cm³ = 1000 kg/m³). The density of oil is therefore 0.820 g/cm³ * 1000 = 820 kg/m³.
The mass m of the oil can be calculated as mass = density × volume. Therefore, m = 820 kg/m³ × 0.550 m³ = 451 kg.
The work W done to lift the oil can be calculated using the formula W = m × g × h, where g is the acceleration due to gravity (9.81 m/s²) and h is the height the oil is being lifted to. Thus, W = 451 kg × 9.81 m/s² × 25.0 m = 110,452.5 J (joules).
The work done by the pump is 110,452.5 J.