Question

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

Part A. Gulls are warm-blooded animals that often have their feet in frigid cold water. Their feet, amazingly, are cold blooded. Let's say that their bodies are about 37 degrees Celcius and their feet are 27 degrees Celcius. How does having cold blooded feet versus warm blooded feet slow down conduction? Assume the size and shape of the feet are the same in both cases. (In this case 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 is stuck to the gull feet by viscous forces.) Gulls are warm-blooded animals that often have their feet in frigid cold water. Their feet, amazingly, are cold blooded. Let's say that their bodies are about 37 degrees Celcius and their feet are 27 degrees Celcius. How does having cold blooded feet versus warm blooded feet slow down conduction? Assume the size and shape of the feet are the same in both cases. (In this case 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 is stuck 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 is smaller.

The length of the barrier is larger

Part B. I have a pair of mittens (where all four fingers are in one "compartment") and a pair of gloves (where each finger has its own "compartment"). Imagine they are both made of the exact same material. My fingers (we won't discuss the thumb) are much warmer in the mittens because I have a pair of mittens (where all four fingers are in one "compartment") and a pair of gloves (where each finger has its own "compartment"). Imagine they are both made of the 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, in part by having a partial vacuum between the inner cylinder and the outer cylinder of the thermos. A partial vacuum is a region with very few gas particles (probably at least 100 times fewer particles than in normal air). How does the presence of a vacuum reduce the rate of conduction? (Assume the size and the shape of the thermos is otherwise the same, and we have the same hot coffee inside and same room temperature outside.) An thermos keeps contents at the same temperature, in part by having a partial vacuum between the inner cylinder and the outer cylinder of the thermos. A partial vacuum is a region with very few gas particles (probably at least 100 times fewer particles than in normal air). How does the presence of a vacuum reduce the rate of conduction? (Assume the size and the shape of the thermos is otherwise the same, and we have the same hot coffee inside and same room temperature outside.)

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

Answer 1

Part A : Rate of Heat transferred Q = KA(T1 - T2)/L

K = Thermal conductivity of barrier i.e water here it will be same

A = Area of cold blooded feet and Warm blooded feet both are same

L = Length of barrier, it will be also same

So, Q is proportional to difference in temperature hence change in temperature of cold feet is less than warm feet as water is also cool. Conduction will slow down.

Ans = The temperature difference between feet and water is smaller.

Part B : Rate of Heat transferred Q = KA(T1 - T2)/L

K = Thermal conductivity of barrier i.e will be same for both mitten and glove

A = Area of Mitten and Glove and both are different i.e mitten area is more

L = Length of barrier, it will be also same

T1 - T2 is same in both case

So, Q is proportional to Area and hence coduction will be more for mitten.

Ans = the area of the barrier is smaller than for gloves

Part C : Rate of Heat transferred Q = KA(T1 - T2)/L

K = Thermal conductivity of barrier will be less because less dense air have less pressure and hence conductivity is very less and it will act like a insulator here.

A = Area of barrier

L = Length of barrier.

So, Q is proportional to K hence, Conduction will slow down.

Ans = The conductivity decreases for a vacuum.