You have an ice cube (H2O) that weighs 5 grams and is at a temperature of -10 degrees Celsius. How much heat energy(in joules) is required to melt the ice cube and raise the temperature of the resulting liquid water to 15 degrees Celsius?

A. 1803 J
B. 2088.5 J
C. 257.5 J
D. 418.2 J

See later post on how to solve.

To calculate the amount of heat energy required to melt the ice cube and raise the temperature of the resulting liquid water, we need to consider two separate processes: one for melting the ice and another for raising the temperature of the liquid water.

1. Melting the ice cube:
The heat energy required to melt the ice can be calculated using the formula:
Q = m * Lf
Where:
Q is the heat energy in joules,
m is the mass of the ice cube in grams, and
Lf is the latent heat of fusion for water, which is 334 J/g.

Given that the mass of the ice cube is 5 grams, we can calculate the heat energy required to melt the ice cube as follows:
Q1 = 5 g * 334 J/g

2. Raising the temperature of the liquid water:
The heat energy required to raise the temperature of the liquid water can be calculated using the formula:
Q = m * Cp * ΔT
Where:
Q is the heat energy in joules,
m is the mass of the liquid water in grams,
Cp is the specific heat capacity of water, which is 4.184 J/g°C, and
ΔT is the change in temperature.

Given that the mass of the liquid water is also 5 grams and the change in temperature is from -10°C to 15°C (ΔT = 15°C - (-10)°C = 25°C), we can calculate the heat energy required to raise the temperature of the liquid water as follows:
Q2 = 5 g * 4.184 J/g°C * 25°C

To get the total heat energy required, we add Q1 and Q2:
Total heat energy = Q1 + Q2

Now, let's calculate the answer:
Q1 = 5 g * 334 J/g = 1670 J
Q2 = 5 g * 4.184 J/g°C * 25°C = 523 J

Total heat energy = 1670 J + 523 J = 2193 J

None of the provided answer choices match the calculated value of 2193 J.