#### Outcome 2

Babies, and especially premature babies, have particularly large surface area relative to their body as compared with adults. That makes them especially susceptible to . Incubators are used to help reduce the in such cases. What are the basic features of an incubator and how do they reduce heat loss by each of the following:

#### Outcome 1

Human body is 98.6 **°F**. Convert this to .

Convert body temperature to .

#### Outcome 3

The surface area of a premature baby can be calculated according to the formula of Haycock *et. al.*^{[1]}

Surface Area = M 0.5378 x L 0.3964 x 0.024265

The result give are in **m ^{2},** but length (L) is input in

**cm**and mass (M) is input in

**kg**

Calculate the surface area for a premature baby with weight of 3.5 **lbs** (a mass of 1.8 **kg**) and length 42 **cm**.

Use the surface area and body temperature you found above to calculate the rate at which the baby loses to the environment by if the room is at a temperature of 75** °F** (23.9 **°C**). The of human skin is typically 0.98. Don’t forget convert the room temperature to .

Calculate the by to the table if the baby is laying on a mattress 5 **cm** thick with of .04 **W**/ (**m °C**). Use the same body temperature and room temperature as in the previous calculations. Assume only the back half of the body is experiencing conduction (use half the surface area).

Calculate the by for an air of 0.5 **m/s** is caused by the ventilation system and movement of people in the room etc. Use the same body temperature and room temperature as in the previous calculations. Assume only the front half of the body is experiencing (use half the surface area).

If the room is at 50 **% ** the air of of 0.5 **m/s** will result in an evaporation from the baby’s moist skin at a rate described by the equation below (we didn’t talk about determining evaporation rate so if you want to understand this equation talk with you instructor, but for now just use it).

Rate of evaporation in **kg/s** = 0.000097 x surface area.

Calculate the rate of evaporation of water from the baby’s skin.

What is the rate at which this evaporation removes thermal energy from the baby? (Hint: How much energy is lost for each **kg** of water that evaporates?)

Add up all of these heat loss rates to get the total .

Assuming the baby is mostly water, (use the of water) calculate the rate at which the of the baby will change in **C°** per second. Use the baby mass from above.

How many degrees would the baby’s body temperature lower in 10 minutes at this rate?

#### Connecting Concepts: Metabolism, Thermal Power, Heat

Let’s imagine that we thought the baby could handle generating the needed to replace the heat loss you calculate above by simply converting food Calories into thermal energy. In that case we wouldn’t need an incubator, we would just need to keep the baby well fed. How much breast milk would the baby need to drink each day? Let’s find out.

Breast milk has 700 Calories (**kcal**) per **kg**. ^{[2]} How many **kg/s** of milk would the baby need to drink to intake the same energy as what is lost?

How many **kg**/hour is this?

How many **kg**/day is that?

How does that compare to the baby’s ?

Does this seem reasonable? Explain.

a measurement of the amount of matter in an object made by determining its resistance to changes in motion (inertial mass) or the force of gravity applied to it by another known mass from a known distance (gravitational mass). The gravitational mass and an inertial mass appear equal.

The condition of having a body temperature well below the normal range.

the amount of heat (thermal energy transferred due to a temperature difference) that leaves an object per unit time

Electromagnetic radiation spontaneously emitted by all objects with temperature above absolute zero.

the process by which heat or directly transmitted through a substance when there is a difference of temperature between adjoining regions, without movement of the material

transfer of heat due to the movement of fluid molecules driven by external factors other than thermal expansion.

vaporization that occurs on the surface of a liquid as it changes into the gas phase

a measure of the average kinetic energy of the particles (e.g., atoms and molecules) in an object, which determines how relatively hot or cold an object feels

the most common relative temperature scale

SI unit of temperature

energy stored in the microscopic motion of atoms and molecules (microscopic kinetic energy)

measure of a material's effectiveness at emitting energy as thermal radiation

a measure of a material's ability to conduct heat

distance traveled per unit time

a measure of how many water molecules are in the vapor phase relative to the maximum number that could possibly be in the vapor phase at at a given temperature. A relative humidity of 100% means that no more water molecules can be added to the vapor phase.

A material property that determines the amount of energy required to raise the temperature one mass unit of the material by one temperature unit.