1.6 Mechanisms of Heat Transfer

Name an example from daily life (different from the text) for each mechanism of heat transfer.

How does the rate of heat transfer by conduction change when all spatial dimensions are doubled?

Explain why using a fan in the summer feels refreshing.

How much greater is the rate of heat radiation when a body is at the temperature $40 ° \text{C}$ than when it is at the temperature $20 ° \text{C}$?

When our bodies get too warm, they respond by sweating and increasing blood circulation to the surface to transfer thermal energy away from the core. What effect will those processes have on a person in a $40.0 - ° \text{C}$ hot tub?

Some electric stoves have a flat ceramic surface with heating elements hidden beneath. A pot placed over a heating element will be heated, while the surface only a few centimeters away is safe to touch. Why is ceramic, with a conductivity less than that of a metal but greater than that of a good insulator, an ideal choice for the stove top?

One way to make a fireplace more energy-efficient is to have room air circulate around the outside of the fire box and back into the room. Detail the methods of heat transfer involved.

When watching a circus during the day in a large, dark-colored tent, you sense significant heat transfer from the tent. Explain why this occurs.

Why are thermometers that are used in weather stations shielded from the sunshine? What does a thermometer measure if it is shielded from the sunshine? What does it measure if it is not?

Your house will be empty for a while in cold weather, and you want to save energy and money. Should you turn the thermostat down to the lowest level that will protect the house from damage such as freezing pipes, or leave it at the normal temperature? (If you don’t like coming back to a cold house, imagine that a timer controls the heating system so the house will be warm when you get back.) Expla…

Broiling is a method of cooking by radiation, which produces somewhat different results from cooking by conduction or convection. A gas flame or electric heating element produces a very high temperature close to the food and above it. Why is radiation the dominant heat-transfer method in this situation?

(a) Calculate the rate of heat conduction through house walls that are 13.0 cm thick and have an average thermal conductivity twice that of glass wool. Assume there are no windows or doors. The walls’ surface area is $120 \text{m}^{2}$ and their inside surface is at $18.0 ° \text{C}$, while their outside surface is at $5.00 ° \text{C}$. (b) How many 1-kW room heaters would be needed to balance the heat transfer due to conduction?

Calculate the rate of heat conduction out of the human body, assuming that the core internal temperature is $37.0 ° \text{C}$, the skin temperature is $34.0 ° \text{C}$, the thickness of the fatty tissues between the core and the skin averages 1.00 cm, and the surface area is $1.40 \text{m}^{2}$.

A man consumes 3000 kcal of food in one day, converting most of it to thermal energy to maintain body temperature. If he loses half this energy by evaporating water (through breathing and sweating), how many kilograms of water evaporate?

(a) What is the rate of heat conduction through the 3.00-cm-thick fur of a large animal having a $1.40 -\text{m}^{2}$ surface area? Assume that the animal’s skin temperature is $32.0 ° \text{C}$, that the air temperature is $−5.00 ° \text{C}$, and that fur has the same thermal conductivity as air. (b) What food intake will the animal need in one day to replace this heat transfer?

Compare the rate of heat conduction through a 13.0-cm-thick wall that has an area of $10.0 \text{m}^{2}$ and a thermal conductivity twice that of glass wool with the rate of heat conduction through a 0.750-cm-thick window that has an area of $2.00 \text{m}^{2}$, assuming the same temperature difference across each.

Some stove tops are smooth ceramic for easy cleaning. If the ceramic is 0.600 cm thick and heat conduction occurs through a 14 cm radius and at a rate of 2256 W, what is the temperature difference across it? Ceramic has the same thermal conductivity as glass and brick.

Many decisions are made on the basis of the payback period: the time it will take through savings to equal the capital cost of an investment. Acceptable payback times depend upon the business or philosophy one has. (For some industries, a payback period is as small as 2 years.) Suppose you wish to install the extra insulation in the preceding problem. If energy cost $\$ 1.00$ per million joules and the in…

What is the percent error of thinking the melting point of tungsten is $3695 ° \text{C}$ instead of the correct value of 3695 K?

How much stress is created in a steel beam if its temperature changes from $–15 ° \text{C}$ to $40 ° \text{C}$ but it cannot expand? For steel, the Young’s modulus $Y = 210 \times 10^{9} \text{N}/\text{m}^{2}$ from Stress, Strain, and Elastic Modulus. (Ignore the change in area resulting from the expansion.)

A mercury thermometer still in use for meteorology has a bulb with a volume of $0.780 \text{cm}^{3}$ and a tube for the mercury to expand into of inside diameter 0.130 mm. (a) Neglecting the thermal expansion of the glass, what is the spacing between marks $1 ° \text{C}$ apart? (b) If the thermometer is made of ordinary glass (not a good idea), what is the spacing?

You leave a pastry in the refrigerator on a plate and ask your roommate to take it out before you get home so you can eat it at room temperature, the way you like it. Instead, your roommate plays video games for hours. When you return, you notice that the pastry is still cold, but the game console has become hot. Annoyed, and knowing that the pastry will not be good if it is microwaved, you warm u…

In some countries, liquid nitrogen is used on dairy trucks instead of mechanical refrigerators. A 3.00-hour delivery trip requires 200 L of liquid nitrogen, which has a density of $808 \text{kg}/\text{m}^{3} .$ (a) Calculate the heat transfer necessary to evaporate this amount of liquid nitrogen and raise its temperature to $3.00 ° \text{C}$. (Use $c_{\text{P}}$ and assume it is constant over the temperature range.) This value is the amount of cooling th…

A 0.800-kg iron cylinder at a temperature of $1.00 \times 10^{3} ° \text{C}$ is dropped into an insulated chest of 1.00 kg of ice at its melting point. What is the final temperature, and how much ice has melted?

Repeat the preceding problem with 0.500 kg of ice, assuming that the ice is initially in a copper container of mass 1.50 kg in equilibrium with the ice.

(a) Calculate the rate of heat conduction through a double-paned window that has a $1.50 -\text{m}^{2}$ area and is made of two panes of 0.800-cm-thick glass separated by a 1.00-cm air gap. The inside surface temperature is $15.0 ° \text{C} ,$ while that on the outside is $−10.0 ° \text{C} .$ (Hint: There are identical temperature drops across the two glass panes. First find these and then the temperature drop across the air gap. This problem ignores t…

For the human body, what is the rate of heat transfer by conduction through the body’s tissue with the following conditions: the tissue thickness is 3.00 cm, the difference in temperature is $2.00 ° \text{C}$, and the skin area is $1.50 \text{m}^{2}$. How does this compare with the average heat transfer rate to the body resulting from an energy intake of about 2400 kcal per day? (No exercise is included.)

An infrared heater for a sauna has a surface area of $0.050 \text{m}^{2}$ and an emissivity of 0.84. What temperature must it run at if the required power is 360 W? Neglect the temperature of the environment.

A pendulum is made of a rod of length L and negligible mass, but capable of thermal expansion, and a weight of negligible size. (a) Show that when the temperature increases by dT, the period of the pendulum increases by a fraction $\alpha d T / 2$. (b) A clock controlled by a brass pendulum keeps time correctly at $10 ° \text{C}$. If the room temperature is $30 ° \text{C}$, does the clock run faster or slower? What is its error in seconds…

In a calorimeter of negligible heat capacity, 200 g of steam at $150 ° \text{C}$ and 100 g of ice at $−40 ° \text{C}$ are mixed. The pressure is maintained at 1 atm. What is the final temperature, and how much steam, ice, and water are present?

Find the growth of an ice layer as a function of time in a Dewar flask as seen in the exercise. Call the thickness of the ice layer L. (a) Derive an equation for dL/dt in terms of L , the temperature T above the ice, and the properties of ice (which you can leave in symbolic form instead of substituting the numbers). (b) Solve this differential equation assuming that at $t = 0$, you have $L = 0 .$ If you have s…

Let’s stop ignoring the greenhouse effect and incorporate it into the previous problem in a very rough way. Assume the atmosphere is a single layer, a spherical shell around Earth, with an emissivity $e = 0.77$ (chosen simply to give the right answer) at infrared wavelengths emitted by Earth and by the atmosphere. However, the atmosphere is transparent to the Sun’s radiation (that is, assume the radiation…