If an iceberg at 0 degrees C has a mass of 200,000,000 kg, how much heat would be required to melt the entire iceberg and raise the melt water to 8.0 degrees C?
q1 = heat to melt the ice berg.
q1 = mass x specific heat x heat fusion.
q2 = meat to raise the temperature to 8C.
q2 = mass water x specific heat water x 8
Total Q = q1 + q2.
To calculate the amount of heat required to melt the entire iceberg and raise the melt water to 8.0 degrees Celsius, we can use the following steps:
Step 1: Calculate the heat required to melt the iceberg
The heat required to melt the ice can be calculated using the equation:
Heat = mass (in kg) × specific heat capacity × temperature change
The specific heat capacity of ice is approximately 2.09 J/g°C.
First, we need to convert the mass of the iceberg from kg to grams:
200,000,000 kg = 200,000,000,000 grams
The temperature change is the difference between the melting point of ice (0°C) and the initial temperature of the iceberg.
Temperature change = 0°C - (- 0°C) = 0°C
Now we can calculate the heat required to melt the iceberg:
Heat = 200,000,000,000 g × 2.09 J/g°C × 0°C
Heat = 0 Joules (no heat required to melt the ice as it is already at 0°C)
Step 2: Calculate the heat required to raise the melt water to 8.0 degrees Celsius
To calculate the heat required to raise the temperature of the melt water, we can use the equation:
Heat = mass (in kg) × specific heat capacity × temperature change
The specific heat capacity of water is approximately 4.18 J/g°C.
First, we need to calculate the mass of the melt water. Since the entire iceberg has melted, the mass of the water will be equal to the mass of the iceberg:
Melt water mass = 200,000,000 kg
The temperature change is the difference between the final temperature (8.0°C) and the initial temperature (0°C):
Temperature change = 8.0°C - 0°C = 8.0°C
Now we can calculate the heat required to raise the melt water to 8.0 degrees Celsius:
Heat = 200,000,000 kg × 4.18 J/g°C × 8.0°C
Heat = 6,688,000,000 Joules (6.688 GJ)
Therefore, the amount of heat required to melt the entire iceberg and raise the melt water to 8.0 degrees Celsius is 6.688 gigajoules.