A 40kg box of sweet cherries at 10 ° c cosisting of 30kg water and 10kg cherries is to be frozen at -30°c.Calculate the total amount of heat that needsto be removed from the cherries . The specific heat capacity of cherries is 3.43kj /kg°c. The specific ccapacity of water is 4.187(use 0°c to -30°c) the specific heat capacity of ice is 2.108kg°c (use for 0°c to -30°c) latent heat of fusion of cherries is 322kj/jg and latent heat of fusion for water is 334kj/kg.
To calculate the total amount of heat that needs to be removed from the cherries, we need to consider the specific heat capacity of both water and cherries, as well as the latent heat of fusion for both cherries and water.
First, let's calculate the heat required to lower the temperature of the water from 10 °C to 0 °C:
Q1 = mass_water * specific_heat_capacity_water * temperature_change_water
= 30 kg * 4.187 kJ/kg°C * (0 °C - 10 °C)
= 30 kg * 4.187 kJ/kg°C * (-10 °C)
= -1256.1 kJ
Next, let's calculate the heat required to freeze the water at 0 °C:
Q2 = mass_water * latent_heat_of_fusion_water
= 30 kg * 334 kJ/kg
= 10020 kJ
Then, let's calculate the heat required to lower the temperature of the solidified water (ice) from 0 °C to -30 °C:
Q3 = mass_water * specific_heat_capacity_ice * temperature_change_ice
= 30 kg * 2.108 kJ/kg°C * (-30 °C - 0 °C)
= 30 kg * 2.108 kJ/kg°C * (-30 °C)
= -1894.6 kJ
Now, let's calculate the heat required to lower the temperature of the cherries from 10 °C to 0 °C:
Q4 = mass_cherries * specific_heat_capacity_cherries * temperature_change_cherries
= 10 kg * 3.43 kJ/kg°C * (0 °C - 10 °C)
= 10 kg * 3.43 kJ/kg°C * (-10 °C)
= -343 kJ
Finally, let's calculate the total amount of heat that needs to be removed from the cherries:
Total Heat = Q1 + Q2 + Q3 + Q4
= -1256.1 kJ + 10020 kJ + (-1894.6 kJ) + (-343 kJ)
= 6757.3 kJ
Therefore, the total amount of heat that needs to be removed from the cherries is 6757.3 kJ.