To find out how many kilograms of paraffin would be needed to collect as much energy as 4.73 x 10^3 kg of water, we can use the formula:
Energy absorbed = mass x specific heat x temperature change
First, we need to calculate the energy absorbed by 4.73 x 10^3 kg of water. Since the specific heat of water is 4.18 J/g°C and we assume the same temperature change for paraffin, we can use the formula:
Energy absorbed by water = mass of water x specific heat of water x temperature change
Plugging in the values:
Energy absorbed by water = 4.73 x 10^3 kg x 4.18 J/g°C x temperature change
Now, we need to calculate the energy absorbed by paraffin. We are given the specific heat of paraffin as 2.90 J/g°C. We need to find the mass of paraffin, so we rearrange the formula:
mass of paraffin = Energy absorbed by paraffin / (specific heat of paraffin x temperature change)
Plugging in the values:
mass of paraffin = Energy absorbed by water / (specific heat of paraffin x temperature change)
mass of paraffin = (4.73 x 10^3 kg x 4.18 J/g°C x temperature change) / (2.90 J/g°C x temperature change)
The temperature change cancels out, and we're left with:
mass of paraffin = (4.73 x 10^3 kg x 4.18 J/g) / 2.90 J
Now, we can calculate the mass of paraffin:
mass of paraffin = (4.73 x 10^3 kg x 4.18 J/g) / 2.90 J
mass of paraffin = 6.82 x 10^3 kg
Therefore, approximately 6.82 x 10^3 kilograms of paraffin would be needed to collect as much energy as 4.73 x 10^3 kilograms of water.