Answer :
First we need to write down heat capacity for water which is constant.
cp=4186 J/(kg*K)
The equation for Energy that we will be calculating is:
E=cp*m*T
where m is mass and T is absolute temperature (273,15 + 60 in this case). Replacing all the values in equation we get:
E = 4186*100*333,15 = 139 456 590 J
cp=4186 J/(kg*K)
The equation for Energy that we will be calculating is:
E=cp*m*T
where m is mass and T is absolute temperature (273,15 + 60 in this case). Replacing all the values in equation we get:
E = 4186*100*333,15 = 139 456 590 J
Method:
To do this problem, we will calculate these three quantities:
- Q₁: Heat needed to raise ice from -273°C to its melting point at 0°C
- Q₂: Heat needed to melt the ice into water
- Q₃: Heat needed to raise that water to 60°C
After we know these quantities, we will add them all together to find the total heat contained in the water.
We will use these two formulas:
Q=mcΔt
- Q is heat
- c is the specific heat of the substance
- m is mass
- Δt is the change in heat
Q=m*Lf
- Q is heat
- m is mass
- Lf is the latent heat of fusion of the substance
Part 1:
To find the heat needed to raise ice from -273°C to its melting point at 0°C, we will use Q=mcΔt.
Q₁=?
m=100kg
c= specific heat of ice = 0.5kcal/kg°C
Δt= final heat - initial heat = (0°C) - (-273°C) = 273°C
Q₁=(100)(0.5)(273)
Q₁=13650kcal
Part 2:
To find the heat needed to melt the ice into water, we will use Q=m*Lf.
Q₂=?
m=100kg
Lf= latent heat of fusion of ice = 79.7kcal/kg
Q₂=(100)(79.7)
Q₂=7970kcal
Part 3:
To find the heat needed to raise the water to 60°C, we will once again use Q=mcΔt.
Q₃=?
m=100kg
c= specific heat of water (not ice anymore!) = 1.00kcal/kg°C
Δt= final heat - initial heat = (60°C) - (0°C) = 60°C
Q₃=(100)(1.00)(60)
Q₃=6000kcal
Part 4:
Now that we finally have Q₁, Q₂, and Q₃, we will add them all together to find the total heat contained in the water.
Recall that:
Q₁=13650kcal
Q₂=7970kcal
Q₃=6000kcal
Q₁+Q₂+Q₃=13650+7970+6000
Total Q = 27620kcal
In scientific notation with three significant figures:
Q = 2.77 x 10⁴ kcal
I hope this helps! Let me know if you have any questions.