The latent heat of fusion for water is given as 335,000 J/kg, and the latent heat of vaporization is 2,260,000 J/kg. To find the mass of water that must be frozen to release a certain amount of heat, we can use the formula:
Q = m × Lf
Where:
- Q is the total heat released (in joules),
- m is the mass of water (in kilograms),
- Lf is the latent heat of fusion (in J/kg).
From this equation, we can rearrange it to solve for mass:
m = Q / Lf
Now, substituting the values for Lf:
m = Q / 335,000
This equation indicates that the mass of water that needs to be frozen depends on the amount of heat Q that you wish to release. Ideally, you would plug in the specific heat quantity you want to release, and you’ll get the mass needed. For example, if you wanted to release 1,000,000 J of heat:
m = 1,000,000 J / 335,000 J/kg ≈ 2.99 kg
Therefore, you would need to freeze approximately 2.99 kg of water at 0°C to release 1,000,000 joules of heat. The concept illustrates how phase changes in water (from liquid to solid) can significantly impact heat transfer due to the high latent heat values.