The latent heat of fusion for water is 33.5 × 104 J/kg, while the latent heat of vaporization is 22.6 × 105 J/kg. What mass m of water at 0 °C must be frozen in order to release the amount of heat that 2.47 kg of steam at 100 °C releases when it condenses?

Mice*Hfwater=2.47*Hvwater

solve for mass ice Mice.

To find the mass of water that needs to be frozen, we need to calculate the heat released when 2.47 kg of steam condenses.

Step 1: Calculate the heat released when 2.47 kg of steam condenses. We can use the latent heat of vaporization formula:

Q = m × L

Where Q is the heat released, m is the mass of steam, and L is the latent heat of vaporization.

Given:
m = 2.47 kg
L = 22.6 × 10^5 J/kg

Q = (2.47 kg) × (22.6 × 10^5 J/kg)
Q = 55.942 × 10^5 J

Step 2: Calculate the mass of water that needs to be frozen. To find the mass, we use the latent heat of fusion formula:

Q = m × L

Where Q is the heat released, m is the mass of water, and L is the latent heat of fusion.

Given:
L = 33.5 × 10^4 J/kg (latent heat of fusion)

Since the heat released when condensing the steam is the same heat absorbed when freezing water, we can equate the two heat values:

Q (heat released when condensing steam) = Q (heat absorbed when freezing water)

(55.942 × 10^5 J) = m × (33.5 × 10^4 J/kg)

Solving for m:

m = (55.942 × 10^5 J) / (33.5 × 10^4 J/kg)

m ≈ 1.66 kg

Therefore, approximately 1.66 kg of water needs to be frozen to release the same amount of heat that 2.47 kg of steam releases when it condenses.