# Heat

Qn 3. The transfer of heat from the body's interior to the surface is achieved primarily through the flow of blood. In cold surroundings blood flow near the skin is reduced by constriction of capillaries. This allows the skin to provide the insulation. Skin temperature can drop to as low as 15 degrees reducing the heat loss from the skin to the environment while the body maintains its normal temperature of about 37 degrees. When your skin temperature is 29 degrees what is the effective average thickness of the insulating layer of tissue separating the skin at 29 degrees from the body interior at 37 degrees. (assume the average surface area of a typical person is 1.5m squared and the average heat transfer is 120 Watts)

Qn 4. A young couple realize that by eating to much ice cream and cake they over ate by about 500 calories. To compensate they want to do an equivalent work climbing stairs or a mountain. How much vertical height must they walk up. (each has a mass of 60 kg. assume that a body transfers energy with the efficiency of 20 %)

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Qn 3. The transfer of heat from the body's interior to the surface is achieved primarily through the flow of blood. In cold surroundings blood flow near the skin is reduced by constriction of capillaries. This allows the skin to provide the insulation. Skin temperature can drop to as low as 15 degrees reducing the heat loss from the skin to the environment while the body maintains its normal temperature of about 37 degrees. When your skin temperature is 29 degrees what is the effective average thickness of the insulating layer of tissue separating the skin at 29 degrees from the body interior at 37 degrees. (assume the average surface area of a typical person is 1.5m squared and the average heat transfer is 120 Watts)

Answer : For heat conduction

H= K S (T1 - T 2) / L

Where H is the heat flow per second

S is the surface area

(T1 - T 2) / L is the temperature gradient and

K= thermal conductivity

120 = K x 1.5 ( 37 - 29)/ L

where L is the effective average thickness of the insulating layer of tissue

No value of K is given.

K can be assumed to be 0.2 W/ m K ( this is the thermal conductivity for human fat ; if any other figure is given in the book it may be substituted)

L= 0.2 X 1.5 X 8 /120= 0.02 metres = 2 cm

Answer 2 cm

Qn 4. A young couple realize that by eating to much ice cream and cake they over ate by about 500 calories. To compensate they want to do an equivalent work climbing stairs or a mountain. How much vertical height must they walk up. (each has a mass of 60 kg. assume that a body transfers energy with the efficiency of 20 %)

They have to burn 1000 calories. ( assuming each overate 500 calories ; the problem is not very clear on this)

1000 calories= 1000 X 4.2= 4200 Joules

Mass= 2 x 60 = 120 Kg

Since the efficiency of transfer of energy is 20 % the work done in climbing up the mountain = 20 % of 4200 Joules= 840 Joules ( The remaining energy is dissipated)

When a mass of m climbs h meters the energy required is mgh where g is the acceleration due to gravity and h is the height .

m g h= 840 Joules

h= 840 / (120 X 9.81)= 0.71 meters

Answer 0.71 meters

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