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
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 processes: the heat energy required to melt the ice cube (known as the heat of fusion) and the heat energy required to raise the temperature of the resulting liquid water (known as the specific heat capacity).
1. Heat energy to melt the ice cube:
The heat of fusion (represented by the symbol "ΔHfus") for water is 334 J/g. This means that it takes 334 joules of heat energy to melt 1 gram of ice at its melting point (0 degrees Celsius). Since our ice cube weighs 5 grams, we can calculate the heat energy required to melt the ice cube by multiplying its mass by the heat of fusion:
Heat energy = mass * ΔHfus
Heat energy = 5 g * 334 J/g
Heat energy = 1670 J
2. Heat energy to raise the temperature of the resulting liquid water:
The specific heat capacity (represented by the symbol "c") for water is 4.18 J/g°C. This means that it takes 4.18 joules of heat energy to raise the temperature of 1 gram of water by 1 degree Celsius. In this case, we need to raise the temperature of the water from -10 degrees Celsius to 15 degrees Celsius, which is a temperature change of 15 - (-10) = 25 degrees Celsius. So, we can calculate the heat energy required to raise the temperature by multiplying the mass of the water by the specific heat capacity and the temperature change:
Heat energy = mass * c * temperature change
Heat energy = 5 g * 4.18 J/g°C * 25°C
Heat energy = 523.5 J
Finally, we add the heat energy required to melt the ice cube and the heat energy required to raise the temperature of the resulting liquid water together:
Total heat energy = heat energy to melt the ice cube + heat energy to raise the temperature
Total heat energy = 1670 J + 523.5 J
Total heat energy = 2193.5 J
Therefore, the correct answer is not listed among the given options.
Use the formula q=mc∆T
Where
m= 5g
∆T=15-(-10)=25
c= 4.186 J/g °C
and solve for q