Final answer:
The amount of heat that must be added to the ice to produce 5 kg of liquid water with a final temperature of 35 °C is 2,683,950 J.
Step-by-step explanation:
To find the amount of heat required to produce 5 kg of liquid water from a 5 kg block of ice at -27 °C to a final temperature of 35 °C, we need to consider the different phases and temperature changes involved.
First, we need to find the heat required to raise the temperature of the ice from -27 °C to 0 °C. We can use the specific heat capacity of ice, which is 2.09 J/g°C. So, the heat required is:
Heat Q₁ = mass × specific heat capacity × temperature change
= 5000 g × 2.09 J/g°C × (0 °C - (-27 °C))
= 279,450 J
This heat will bring the ice to its melting point. To melt the ice, we need to use the latent heat of fusion, which is 334 J/g. So, the heat required to melt the ice is:
Heat Q₂ = mass × latent heat of fusion
= 5000 g × 334 J/g
= 1,670,000 J
After melting, the water needs to be heated from 0 °C to 35 °C. We can use the specific heat capacity of water, which is 4.18 J/g°C. So, the heat required is:
Heat Q₃ = mass × specific heat capacity × temperature change
= 5000 g × 4.18 J/g°C × (35 °C - 0 °C)
= 734,500 J
To find the total heat required, we can add up the individual heats:
Total heat = Q₁ + Q₂ + Q₃
= 279,450 J + 1,670,000 J + 734,500 J
= 2,683,950 J
Therefore, the amount of heat that must be added to the ice is 2,683,950 J.