Dimension Analysis -Turkey Cooking

[S-Ragnork1729]

Homework Statement

Each year on their Thanksgiving holiday Americans consume some 50 million turkeys .Unlike chickens, which have been bred to uniform size, turkey weights vary over an order of mag-nitude. Wild turkey hens weigh as little as 3 kilograms while domestic ones weigh as much as 36 kilograms. So the question arises, “How long should we cook our turkey? Last year our 9 kilogram turkey was perfect after 4 hours. This year we have a 6-kilogram turkey ?”

Relevant Equations

Dimension Analysis

I think cooking time $t$ is proportional to mass $m$ of the turkey .

 

[phyzguy]

Two comments:
(1) Since this is about dimensional analysis, you should include the units in your calculations. What are the units of a, for example?
(2) How do you know that the cooking time is linearly related to the mass? For example, the cooking time could depend on the square of the mass.

 

[kuruman]

Homework Statement: Each year on their Thanksgiving holiday Americans consume some 50 million turkeys .Unlike chickens, which have been bred to uniform size, turkey weights vary over an order of mag-nitude. Wild turkey hens weigh as little as 3 kilograms while domestic ones weigh as much as 36 kilograms. So the question arises, “How long should we cook our turkey? Last year our 9 kilogram turkey was perfect after 4 hours. This year we have a 6-kilogram turkey ?”
Relevant Equations: Dimension Analysis

I think cooking time $t$ is proportional to mass $m$ of the turkey .

Dimension Analysis is not an equation.

According to our rules, to receive help, you need to show some credible effort towards answering the question.
Please read, understand and follow our homework guidelines, especially item 4, here
https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

 

[Orodruin]

Is this the spherical turkey thread?

Doing dimensional analysis here requires actually understanding somewhat how heat transfer works. Still, OP also needs to provide some actual dimensional analysis. Obviously time and mass are of different dimension so some further parameters with other dimensions are necessary. OP should consider what these may be assumed to be.

 

[WWGD]

Homework Statement: Each year on their Thanksgiving holiday Americans consume some 50 million turkeys .Unlike chickens, which have been bred to uniform size, turkey weights vary over an order of mag-nitude. Wild turkey hens weigh as little as 3 kilograms while domestic ones weigh as much as 36 kilograms. So the question arises, “How long should we cook our turkey? Last year our 9 kilogram turkey was perfect after 4 hours. This year we have a 6-kilogram turkey ?”
Relevant Equations: Dimension Analysis

I think cooking time $t$ is proportional to mass $m$ of the turkey .

Any chance you have data on cooking time vs weight?

 

[kuruman]

In the mid seventies I had a subscription to the Journal of Irreproducible Results (paper edition) in which I remember reading the description of an experiment in which a frozen turkey was dropped many times from a fixed height $h$ in an attempt to cook it. I remember seeing a graph of turkey temperature vs. time with the temperature reaching asymptotically a final value. In keeping with the spirit of the journal in which this article was published, the graph axes were not labeled with numerical values.

Fast forward to today. I searched for a mention of this experiment on the web and I found this gem generated by AI (see screenshot below). I love the explanation why it doesn't work; there is humor in humorlessness.

I also found an article by Rhett Allian, a physicist. He calculates the height needed to cook a frozen spherical turkey in a single drop. The method of cooking is not conversion of $mgh$ into $kT$ (the method in the original J. Irrep. Res. article) but air resistance as the turkey falls through the atmosphere.

 

[berkeman]

"Oh the humanity!"

Spoiler

Oh wait, those were live turkeys...

 

[phinds]

Turkey stories always remind me of the one about the elderly dowager lady who went into the grocery store to get a really big turkey for her really big family and, not finding one big enough, asked the young butcher "Young man, do these turkeys get any bigger". He replied with some horror "NO MA'AM ... THOSE TURKEYS ARE DEAD !"

 

[phinds]

I think cooking time is proportional to mass of the turkey .

Nature and science really don't care what you think. How about some facts to back up your opinion? What research have you done?

 

[Chestermiller]

What physical parameters besides mass do you envision as playing a role in determining the cooking time of a turkey?

 

[Chestermiller]

See Transport Phenomena, Bird, Stewart, and Lightfoot, Problem 12.B-7, Timetable for Roasting Turkey

 

[MidgetDwarf]

What level are you in? If its an Algebra class. Answer changes depending on level.

Ie., for a simple algebra level.
Its equivalent to finding the unit cost.

Say 3lb of bananna cost $2.00. How much is 5lb of banannas.

If physics. Asumme Turkey is spherical. Assume turkey is cooked evenly in over. We can put further constraints., what temperature is turkey ussually cooked at...

Show a bit of effort, and ill update my response.

 

[Orodruin]

Ie., for a simple algebra level.
Its equivalent to finding the unit cost.

Someone is about to burn a turkey …

If physics. Asumme Turkey is spherical. Assume turkey is cooked evenly in over. We can put further constraints., what temperature is turkey ussually cooked at...

This is not very relevant given the input and expected output. It is a simple dimensional analysis problem once you have identified the correct parameters (assuming scaling properties hold for turkeys).

On a more practical note, the OP has not been seen since a couple of hours after making the post and has already had several requests for clarification and detail without providing such. I suggest we chill a little bit and await for OP to provide - if they want to continue the thread. Otherwise it just risks being a lot of regulars posting their own takes …