Step-by-step explanation:
To calculate the amount of heating oil needed, we need to first determine the amount of energy required to heat the water. We can use the formula for calculating the energy required to heat a substance:
Q = mcΔT
where
Q is the energy required,
m is the mass of the substance,
c is the specific heat capacity of the substance, and
ΔT is the change in temperature.
For water, the specific heat capacity is 4.18 J/g°C.
Plugging in the values:
Q = 245 kg * 4.18 J/g°C * (68.0°C - 12.0°C) = 45,082,000 J
Next, we need to consider the efficiency of the boiler. The boiler is only 62% efficient, which means that only 62% of the energy released from the heating oil will actually be used to heat the water.
So the actual amount of energy required from the heating oil would be:
Q / 0.62 = 45,082,000 J / 0.62 = 72,619,355 J
Finally, we can use the heat energy released by 1 kg of heating oil to calculate the mass of heating oil required:
72,619,355 J / (4.15 x 107 J/kg) = 17.5 kg
So the boiler would need approximately 17.5 kg of heating oil to heat 245 kg of water from 12.0°C to 68.0°C.