You have an ice cube (H2O) that weighs 5 grams and is at a temperature of 20 degrees Celsius. How many 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
Q=mc?T where ?T is the change in temperature in degrees, m is the mass in grams and c is the specific heat capacity of water.
To calculate the total amount of energy required to melt the ice cube and raise the temperature of the resulting liquid water, we need to consider two processes: the heat required for phase change (melting) and the heat required to change the temperature of the water.
First, let's calculate the amount of energy required to melt the ice cube. The heat required for phase change (melting) is given by the equation:
Q = m * ΔH
where Q is the energy, m is the mass, and ΔH is the heat of fusion (energy required to change the phase of the substance).
The heat of fusion for water is approximately 334 J/g. So, the energy required to melt the ice cube can be calculated as:
Q_melt = m * ΔH_melt
= 5 g * 334 J/g
= 1670 J
Next, let's calculate the amount of energy required to change the temperature of the liquid water. The heat required to change the temperature of a substance is given by the equation:
Q = m * c * ΔT
where Q is the energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
The specific heat capacity of water is approximately 4.18 J/g·°C. So, the energy required to raise the temperature of the liquid water can be calculated as:
Q_temp = m * c * ΔT
= 5 g * 4.18 J/g·°C * (15 °C - 0 °C)
= 313.5 J
Finally, the total energy required is the sum of the energy required for phase change and the energy required for temperature change:
Total energy = Q_melt + Q_temp
= 1670 J + 313.5 J
= 1983.5 J
Therefore, the correct answer is B. 2088.5 J (the closest option to 1983.5 J).