A solar heating specialist is considering paraffin as a possible solar heat collector. How many kilograms of paraffin would be needed to collect as much energy as 4.73 x 10^3 kg of water? The specific heat of paraffin is 2.90J/gxC. Hint: Assume the same temperature change.
You know by reasoning that it will be 4.18/2.90 = 1.44 x mass H2O
I would do this.
q for paraffin = mass P x specific heat x delta T.
q for H2O = 4730 x specific heat x delta T.
Set them equal.
mass P x 2.90 x delta T = 4730 x 4.18 x delta T.
mass paraffin = 4730 x 4.18/2.90 = ? and convert to kg and round.
The specific heat of water is 4.18*10^3 J/g*C.
The product of mass and specific heat would be the same for water and paraffin, for constant deltaT and energy content
The amount of paraffin needed to store the same heat as that amount of water would be higher by a factor
4.18/2.90 = 1.441
This assumes that the paraffin does not melt. A phase change would help store energy.
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.