# 92 Unit 9 Review, Practice, and Assessment

### Learner Objectives

- Explain how heat transfer by conduction, convection, radiation, and evaporation occur on a microscopic scale. [2]
- Explain strategies for slowing each type of heat transfer. [2]
- Apply the concepts of temperature, heat capacity, and latent heat to predict temperature changes in response to heat transfer. [3]

### Outcome 1

1) Use a microscopic model for how conduction happens to explain why two objects must be in contact in order for conduction to occur.

2) Use a microscopic model for how conduction happens to explain why convection happens in fluids, but not in solids.

3) Explain how radiation can transfer heat even when conduction and convection cannot.

4) When molecules evaporate they take their share of thermal energy with them. The fluid now has less energy, but it also has fewer molecules, so it seems like maybe the average energy per molecule might not have changed, so the liquid temperature might not have changed. Explain why evaporation can leave the remaining liquid cooler.

### Outcome 2

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

b) Conduction

d) Evaporation

### Outcome 3

Through the following questions we will investigate heat loss and temperature change for a premature baby in the absence of an incubator.

6) Human body temperature is 98.6 **°F**. Convert this to Celsius.

7) Convert body temperature to Kelvin.

8) 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

Note that the result given is in **m ^{2},** but length (L) is input in

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

**kg**

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

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

9) Calculate the heat loss rate by conduction to the table if the baby is laying on a mattress 5 **cm** thick with thermal conductivity 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).

10) Calculate the heat loss rate due to forced convection for an air speed 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 forced convection (use half the surface area).

11) If the room is at 50 **% **relative humidity the air speed 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.

12) 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?)

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

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

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

16) Let’s imagine that we thought the baby could handle generating the thermal energy 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. Let’s investigate if this is possible by calculating how much breast milk the baby would need to consume each day.

a) 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?

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

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

d) How does that compare to the baby’s mass?

e) Does this seem like a reasonable amount of milk for the baby to consume and digest each day? 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.

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

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

SI unit of temperature

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.