Heat conduction from a hotter object to a colder object througha barrier (e.g. warm inside out to cold outside air through awindow) is descrbed by Q?t=kAL|T1?T2| where k is the conductivityof the barrier, L is the distance the heat has to travel betweenhotter and colder objects, A is the total cross sectional area ofthe barrier that is perpendicular to heat flow, and T1 and T2 arethe two temperatures. In this problem, you will connect real lifesituations to this equation.

Part A. Gulls are warm-blooded animals that often have theirfeet in frigid cold water. Their feet, amazingly, are cold blooded.Let's say that their bodies are about 37 degrees Celcius and theirfeet are 27 degrees Celcius. How does having cold blooded feetversus warm blooded feet slow down conduction? Assume the size andshape of the feet are the same in both cases. (In this case the hotobject is the gull foot, the cold object is the water, and thebarrier we can take as the thin layer of water that is stuck to thegull feet by viscous forces.) Gulls are warm-blooded animals thatoften have their feet in frigid cold water. Their feet, amazingly,are cold blooded. Let's say that their bodies are about 37 degreesCelcius and their feet are 27 degrees Celcius. How does having coldblooded feet versus warm blooded feet slow down conduction? Assumethe size and shape of the feet are the same in both cases. (In thiscase the hot object is the gull foot, the cold object is the water,and the barrier we can take as the thin layer of water that isstuck to the gull feet by viscous forces.)

The conductivity of the water barrier has decreased.

The area of the feet is smaller.

The temperature difference between feet and water issmaller.

The length of the barrier is larger

Part B. I have a pair of mittens (where all four fingers are inone \"compartment\") and a pair of gloves (where each finger has itsown \"compartment\"). Imagine they are both made of the exact samematerial. My fingers (we won't discuss the thumb) are much warmerin the mittens because I have a pair of mittens (where all fourfingers are in one \"compartment\") and a pair of gloves (where eachfinger has its own \"compartment\"). Imagine they are both made ofthe exact same material. My fingers (we won't discuss the thumb)are much warmer in the mittens because

the area of the barrier is smaller than for gloves
the conductivity of the barrier is smaller than for gloves
the length of the barrier is larger than for gloves

Part C. An thermos keeps contents at the same temperature, inpart by having a partial vacuum between the inner cylinder and theouter cylinder of the thermos. A partial vacuum is a region withvery few gas particles (probably at least 100 times fewer particlesthan in normal air). How does the presence of a vacuum reduce therate of conduction? (Assume the size and the shape of the thermosis otherwise the same, and we have the same hot coffee inside andsame room temperature outside.) An thermos keeps contents at thesame temperature, in part by having a partial vacuum between theinner cylinder and the outer cylinder of the thermos. A partialvacuum is a region with very few gas particles (probably at least100 times fewer particles than in normal air). How does thepresence of a vacuum reduce the rate of conduction? (Assume thesize and the shape of the thermos is otherwise the same, and wehave the same hot coffee inside and same room temperatureoutside.)

The conductivity decreases for a vacuum
The cross sectional area of the barrier increases for avacuum.
The length of the barrier increases for a vacuum.
The temperature difference increases for a vacuum.