117k views
2 votes
A busy housewife left 25 g of ice in an open insulated container while she was answering her cellphone. When she returned, the ice at 0 ºC was converted to water at 3.0 ºC. Calculate the energy needed for the ice to totally melt ad reach its present temperature specific heat capacity of water = 4200 J/kgK Specific Latent heat of fusion of Ice = 340 000J/Kg *?

1 Answer

4 votes

Final answer:

The energy required to melt 25 g of ice and increase the water temperature to 3.0 ºC is 8,815 J, which involves the latent heat of fusion and the specific heat capacity of water.

Step-by-step explanation:

A busy housewife left 25 g of ice in an open insulated container, which then transformed into water at 3.0 ºC from its initial state of 0 ºC. To calculate the energy needed for the ice to totally melt and reach this temperature, we consider two processes: the melting of ice and the heating of the resulting water.

The specific latent heat of fusion of ice (α) is 340,000 J/kg, and the specific heat capacity of water (β) is 4,200 J/kgK.

To melt the ice, the energy required (Q1) is given by:

Q1 = m×α

where 'm' is the mass of the ice.

For the 25 g (0.025 kg) of ice:

Q1 = 0.025 kg × 340,000 J/kg = 8,500 J

After melting, the ice becomes water at 0 ºC. Now, to increase the temperature to 3.0 ºC, we use the equation:

Q2 = m×β×ΔT

where ΔT is the change in temperature. Q2 = 0.025 kg × 4,200 J/kgK × 3 K = 315 J

The total energy required is the sum of Q1 and Q2:

Total energy (Q) = Q1 + Q2 = 8,500 J + 315 J = 8,815 J

Hence, the energy needed to melt 25 g of ice and then increase the temperature of the water to 3.0 ºC is 8,815 J.\

User Kontiki
by
8.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.