How much heat is required to change 2.5kg of ice at 0.0 degrees C to water at 50 degrees C?
56J
To calculate the amount of heat required to change a substance from one state to another, we need to know the specific heat capacity and the heat of fusion/vaporization. In this case, we are changing ice to water, so we will need to consider the heat of fusion.
The process can be divided into two parts:
1. Heating the ice from 0.0 degrees Celsius to its melting point (0.0 degrees Celsius).
2. Melting the ice at 0.0 degrees Celsius to water at 0.0 degrees Celsius.
3. Heating the water from 0.0 degrees Celsius to 50 degrees Celsius.
Let's go step by step:
1. Heating the ice from 0.0 degrees Celsius to its melting point:
The specific heat capacity of ice is 2.09 J/g°C. Since we have 2.5 kg of ice, we need to convert it to grams:
2.5 kg x 1000 g/kg = 2500 g.
The temperature change is 0.0°C. Hence, the heat required is calculated using the formula:
Heat = mass x specific heat capacity x temperature change.
Heat = 2500 g x 2.09 J/g°C x (0.0°C - 0.0°C)
Heat = 0 Joules.
2. Melting the ice at 0.0 degrees Celsius to water at 0.0 degrees Celsius:
The heat of fusion (melting) for ice is 334 J/g. We already know the mass of the ice (2500 g).
Heat = mass x heat of fusion.
Heat = 2500 g x 334 J/g
Heat = 835,000 Joules.
3. Heating the water from 0.0 degrees Celsius to 50 degrees Celsius:
The specific heat capacity of water is 4.18 J/g°C. We still have 2500 g of water, and the temperature change is 50°C.
Heat = mass x specific heat capacity x temperature change.
Heat = 2500 g x 4.18 J/g°C x 50°C
Heat = 522,500 Joules.
To find the total heat required, we sum up the heats from the three steps:
Total heat = Heat from step 1 + Heat from step 2 + Heat from step 3
Total heat = 0 Joules + 835,000 Joules + 522,500 Joules
Total heat = 1,357,500 Joules
Therefore, it would require 1,357,500 Joules of heat to change 2.5 kg of ice at 0.0 degrees Celsius to water at 50 degrees Celsius.