1. In a physics experiment, 425 g of lead shot at 220.0 °C is added to 550 g of water at 16.0° C in an insulated thermos. What is the final temperature of the lead and water?

2. In another physics experiment, 75 g of ice at -20.0 °C is added to 1350 g of water at 80.0 °C in an insulated thermos. What is the final temperature of the water?
   

3. A student's 250 g coffee has cooled to 30 °C while he has been studying. He decides to reheat the coffee by placing it in his 300 W microwave. How long does he need to set the microwave for, if he wishes to heat the coffee to 70 °C. Treat the coffee as being water and assume it absorbs all the microwave's energy. Recall that power is energy output over time.
   

4. When you exercise, you produce lots of thermal energy internally. If you don't dissipate the heat, your core temperature would rise dangerously high. During heavy exercise you may need to dissipate hundreds of extra watts of thermal energy. Suppose that your core is at 37 °C and your skin is at 34 °C. Assume that you have on average 3 cm of fat and a surface area of 1.5 m². Take the thermal conductivity of body fat to be 0.20 J/(s·m·C). What is the rate of heat loss through your skin? Will you need other ways of cooling down?

5. Another way your body has of cooling is by flushing - warm blood is sent to the surface arteries and this blood cools down quicker because there is so little fat in the way. The cool blood returns to the core to collect more thermal energy and to repeat the process. An even more powerful way of cooling down is sweating. The sweat (basically water at skin temperature) will evaporate carrying energy away from the body. If a person is exercising and producing an extra 250 W of thermal energy, what maximum mass of sweat does the person produce in an hour? Note that evaporation occurs best into dry air, so when it is very humid sweating does not cool very effectively.

6. A wall has a area of 10 m². It is 3.00 cm thick polyurethane (κ = 0.024 J/s·m·K) on 1.00 cm of wood (κ = 0.010 J/s·m·K). The interior is 22 °C and the exterior is 5 °C. What is the temperature at the boundary between the polyurethane and the wood?

7. Triple-glazed glass consists of three 0.25 cm thick panes of glass separated by two air gaps of 1.00 cm thickness. What is the effective R-value of this window? Note κ_glass = 1.0 W/m·K and κ_air = 0.026 W/m·K.
   

8. A cabin has a surface area of 90 m². The cabin is made of 2.5 cm thick wood with a thermal conductivity of 0.13 W/m-K. What is the R-value of the wood? If the exterior temperature is -10 °C, what would have to be the power of a space heater to keep the interior at 17 °C? If the cabin was also insulated with 2.4 cm of fibreglass (κ = 0.048 W/m-K), what would be the necessary power of the space heater? What would be the temperature of the interface between the fibreglass and the wood?
   

9. A matte (i.e. dull) black cube has a side length of 20.0 cm. It is suspended in 20 °C still air. It is absorbing sunlight at a rate of 400 W/m² from the Sun directly overhead. What will be its final equilibrium temperature if it only loses energy by radiation? If the cube was shiny white, and reflected 60% of the sunlight, what would its final temperature be?

10. If you stand naked in a room, your skin and the walls of the room will exchange heat by radiation. Suppose the temperature of your skin is 33° C, the surface area of your skin is 1.5 m², and the temperature of the walls is 15° C. Assume that your body and the walls act as blackbodies.
    (a) What is the rate at which your body radiates heat?
    (b) What is the rate at which your skin absorbs heat?
    (c) What is the net rate of your loss of heat?
    (d) How many Oh Henry! bars (1338 kJ per bar) would you have to eat in a day to survive?
    

11. Assume the naked person in the above question would feel comfortable at a metabolic rate of 100 W. What would the room temperature have to be for him to feel comfortable?

12. For the same person in Question 10, they decide to put on a wool catsuit or leotard (i.e. something tight and clingy so there is no layer of air), κ = 0.040 W/m·K, to stay comfortable. What will be the temperature of the surface of the catsuit? How thick must the catsuit be? Note that the net thermal energy from the person must pass through the catsuit by conduction before being radiated away at the surface of the catsuit.

13. Suppose the room temperature is Question 10 is 25 C, slightly warmer than comfortable. The person flushes to cool down. In flushing, warm blood is brought to the surface of the skin raising skin temperature. The blood returning from the skin to the core will be cooler than before flushing will also cool the person but ignore that effect. Find the new skin temperature if the person is comfortable (has a metabolic rate of 100 W)?

14. Suppose the room temperature is Question 10 is 30 C, warmer than comfortable.  The person sweats to cool off. How many grams of sweat will be produced in one hour if the person's metabolic rate is to stay at 100 W?

15. The sun is 150 × 10⁹ m from the earth. The surface temperature of the sun is 5776 K.
    

    (a) The flux (or power per unit area) of sunlight at the earth is 1.34 × 10³ W/m². Determine the total power emitted by the sun. The surface area of a sphere is 4πr².
    (b) Calculate the radius of the sun. Assume that the sun is a blackbody.
    (Note - Astronomers determine the surface temperature of a star from its colour. In this way they can determine the radii of stars by measuring the flux of starlight.)

16. Suppose that your core is at 37 °C and the ambient or air temperature is 5 °C. The temperature of your skin is determined by how the rate energy is conducted through your skin from the core to your skin and the rate at which you can emit thermal radiation to the environment. (We are neglecting the insulating properties of the air and any wind chill). Assume that you have on average 3 cm of fat and a surface area of 1.5 m². Take the thermal conductivity of body fat to be 0.20 J/(s·m·°C). Find your skin temperature to 3 significant figures. You will need to try some values (say 25 °C and 20 °C) and then try new values to get to the correct answer. Assume you are a blackbody.

17. The person in the previous problem will cool rapidly since a typical 70 kg person generates 100 W of heat. To keep warm, one can engage in physical activity. How much heat must he generate? What amount of physical activity (work) must he do? Luckily this person is hill climbing, at what rate (in metres per second and metres per hour) must he climb? Assume that he is 25% efficient?

18. A kg of ice fills a cube 10 cm on each side. Suppose the ice is at 0 C and the ambient temperature is 20 C. How long will it take to melt completely to water at 0 C?

Questions? mike.coombes@kpu.ca