Question

A 7 kg (about 15 pound) frozen turkey at -10°C is placed in boiling water to cook (do not do this at home). Assume that the cooker is sealed and insulated. How much boiling water must be placed in the cooker with the turkey so that the turkey reaches a final temperature of 74°C and is safe to eat. Latent heat of fusion of poultry is 247 kJ/kg. Specific heat of turkey is 2.81 kJ/kg °C. Specific heat of water is 4180 J/kg °C. Latent heat of vaporization of water is 2256 kJ/kg.

Answer 1

To cook the turkey, approximately 31.11kg of boiling water is necessary to provide enough heat to warm the turkey to 0°C, melt it, and then heat it up to 74°C.

Step-by-step explanation:

To determine how much boiling water is needed to bring a 7 kg turkey from -10°C to 74°C, we need to calculate the heat required to warm the turkey to 0°C, melt it (since it is frozen), and then heat it to 74°C. Afterward, we'll need to find out how much heat that amount of boiling water can supply without cooling below 100°C.

First, calculate the heat needed to warm the turkey to 0°C: Q1 = mass·specific heat·ΔT = 7 kg· 2.81 kJ/kg°C·(0 - (-10)) = 196.7 kJ.

Next, calculate the heat required for the phase change: Q2 = mass·latent heat of fusion = 7 kg· 247 kJ/kg = 1729 kJ.

Then, calculate the heat to raise the temperature to 74°C: Q3 = mass·specific heat·ΔT = 7 kg· 2.81 kJ/kg°C·(74 - 0) = 1451.4 kJ.

The total heat required: Qtotal = Q1 + Q2 + Q3 = 196.7 kJ + 1729 kJ + 1451.4 kJ = 3377.1 kJ.

Now, calculate the mass of boiling water needed, knowing the specific heat of water and that it will cool from 100°C to final temperature of turkey which is 74°C:

Qwater = mass of water·specific heat of water·ΔT

3377.1 kJ = mass of water· 4.18 kJ/kg°C·(100 - 74)

Mass of water = 3377.1 kJ / (4.18 kJ/kg°C · 26°C) = 31.11 kg

Therefore, approximately 31.11 kg of boiling water is necessary.