Cooking Time Of Chickens

Classical Mechanics Level 5

A recipe book indicates that the cooking time of a chicken of \(1\text{ kg}\) is 1 hour, and you need to cook a chicken of \(2 \text{ kg}\).

  • The chickens are modeled as uniform solid spheres of density \( \rho \), thermal conductivity \( \kappa \), and initial temperature \( T_{0} \).
  • The temperature of the hooven \( T_{H} \) is the same for cooking a chicken of 1 kg or 2 kg.
  • The chickens are cooked when the temperature of the center reaches a certain value \(T_c\), where \( T_{0} < T_{c} < T_{H} \). This value is the same for 1 kg and 2 kg chickens.

What is the cooking time of your \(2\text{ kg}\) chicken? Express your answer in minutes, rounded to the nearest integer.


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