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.
100000 billion
To determine 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: melting the ice and heating the liquid water.
1. Melting the Ice:
To calculate the heat energy required to melt the ice cube, we can use the formula: Q = m * Heat of Fusion (Hf).
The formula tells us that the amount of heat energy (Q) required to change the state of a substance is equal to the mass (m) multiplied by the specific heat of fusion (Hf) for that substance.
For water, the specific heat of fusion 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:
Q1 = 5 g * 334 J/g = 1670 J.
So, the heat energy required to melt the ice cube is 1670 J.
2. Raising the Temperature of the Liquid Water:
To calculate the heat energy required to raise the temperature of the liquid water from -10 degrees Celsius to 15 degrees Celsius, we can use the formula: Q = m * c * ΔT.
The formula tells us that the amount of heat energy (Q) required to change the temperature of a substance is equal to the mass (m) multiplied by the specific heat capacity (c) of the substance multiplied by the change in temperature (ΔT).
For water, the specific heat capacity is approximately 4.184 J/g°C.
Given that the mass of the liquid water is also 5 grams and the change in temperature is 25°C (15°C - (-10°C)), we can calculate the heat energy required to raise the temperature:
Q2 = 5 g * 4.184 J/g°C * 25°C = 523 J.
So, the heat energy required to raise the temperature of the liquid water is 523 J.
Finally, to get the total heat energy required, we add the heat energy required to melt the ice cube (Q1) and the heat energy required to raise the temperature of the liquid water (Q2):
Total heat energy = Q1 + Q2 = 1670 J + 523 J = 2193 J.
Now, let's compare this result with the given answer choices:
A. 1803 J
B. 2088.5 J
C. 257.5 J
D. 418.2 J
Since 2193 J is not provided as an answer choice, the closest option is B. 2088.5 J.
Therefore, the closest correct answer would be B. 2088.5 J.