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Chapter 14 Temperature and Heat Objectives ● To study temperature and temperature scales ● To describe thermal expansion and its applications ● To explore and solve problems involving heat, phase changes and calorimetry ● To study heat transfer
14.1 Temperature and Thermal Equilibrium
● Temperature is an attempt to measure the “hotness” or “coldness” on a scale you devise. ● A device to do this is called a thermometer and is usually calibrated by the melting and freezing points of a substance. This is most often water with corrections for atmospheric pressure well known. ● The thermometer is often a container filled with a substance that will expand or contract as heat flows in its surroundings. Thermal Equilibrium ● If two objects are different temperatures are placed in contact, heat will always flow from hotter to colder. This will continue until both objects are at the same temperature. This condition of stability is called thermal equilibrium. ● Two systems are in thermal equilibrium if and only if they have the same temperature. ● When heat flow is considered, some materials, like metals, are good transmitters of heat energy. We term these materials to be thermal conductors. ● Materials like styrofoam are poor conductors of heat and will, in fact, severely restrict heat flow. Materials that conduct heat energy poorly are called insulators. What’s Behind Temperature ● We will learn more about it in the next lectures, but temperature is a measure of (thermal) energy contained in the object ● It is directly related with the motion of microscopic particles that make up the object ○ Molecules of gas ○ Atoms in the crystal lattice of metal ● The Zeroth Law of Thermodynamics ● If A is in thermal equilibrium with C and B is in thermal equilibrium with C then A is in thermal equilibrium with B…
● Two systems are in thermal equilibrium if and only if they have the same temperature. ●
14.2 Temperature Scales
● Based on the boiling and freezing points of water, two systems developed to measure temperature. ★ Fahrenheit and Celscius temperature scale ○ In the United States, the Fahrenheit scale is used with boiling at 212F and freezing at 32F. ○ In many other countries, the Celsius (also called Centigrade) scale is used with water freezing at 0C and boiling at 100C. ○ Conversion between Fahrenheit and Celscius ■ ★ Kelvin Scale ● Scientists experimenting with gases noted a linear behavior between pressure and temperature. Using various gases, the linear plots were all noted to converge at the same place ○ ● Named for its inventory, Lord Kelvin (1827-1907), the kelvin scale took this point to be the absolute zero of all temperatures, the point at which everything is a solid and all motion ceases. ★ Temperature Conversions ● Be comfortable converting between the different temperature scales. Example 14.1 Body Temperature ● Simple temperature unit conversion question ● Normal internal body temperature for an average healthy human is 98.6F. a) Find this temperature in degrees Celsius and in kelvins i)
An interesting Behavior — 14. ● When you heat an object that has a hole in it, the hole gets bigger. ● This figure shows what happens. If you heat a flat plate of material, its area increases. If you now cut a section from the center of the plate, both the cutout and the remaining plate (with a hole in it) behave as they did previously: the cutout piece and the hole it came from both got bigger. Example 14.2 Change in length of a measuring tape ● See how thermal expansion can actually throw off the accuracy of a length-measuring device (a tape measure). ● A surveyor uses a steel measuring tape that is exactly 50.000 m long at a temperature of 20C. What is its length on a hot summer day when the temperature is 35C? ● Solve: ○ ○ The new length is: Volume Expansion ● When the temperature of an object changes, the change in volume is proportional to the temperature change and to the initial volume (most of the time) ● Formula ○ and ● β is coefficient of volume expansion ● v(0) is initial volume ● Units of β: K^-1, C^0- ● For solid materials that expand equally in all direction: β=3α ○ Example 14.4 Expansion of Mercury ● Comparing volume expansion of a liquid with volume expansion of vessel that holds liquid question ● A glass flask with a volume of 200cm^3 is filled to the brim with mercury at 20C. When the temperature of the system is raised to 100C, does the mercury overflow the flask? If so, by how much? The coefficient of volume expansion of the glass is 1.2 x 10^-5 K^-1. ● Solve:
Thermal Expansion of Water ● Water is different and this is important! ● If water behaved like most substances, contracting continuously on cooling and freezing, lakes would freeze from the bottom up. Circulation due to density differences would continuously carry warmer (less dense) water to the surface for efficient cooling, and lakes would freeze solid much more easily. ● Figure 14.9 — the volume of 1 g of water in the temperature range from 0C to 10C. The fact that water is denser at about 4C than at the freezing point is vitally important for the ecology of lakes and streams. Thermal Stress ● If we clamp the ends of a rod rigidly to prevent expansion or contraction and then raise or lower the temperature, a compressive or tensile stress called thermal stress develops. ● To calculate the thermal stress in a clamped rod, we compute the amount the rod would expand (or contract) if it were not held and then find the stress needed to compress (or stretch) it back to its original length. Example 14.5 Stress on a spacer ● An aluminum cylinder 10 cm long with a cross-sectional area of 20cm^2, is to be used as a spacer between two steel walls. At 17.2C, it just slips in between the walls. Then it warmsto 22.3C. Calculate the stress in the cylinder and the total force it exerts on each wall, assuming that the walls are perfectly rigid and a constant distance apart. ● Solve: ○ Stress: ■ ○ Total force F exerted by the cylinder on a wall is
● At any given pressure there is a unique temperature at which liquid water and ice can coexist in a condition called phase equilibrium. ● More generally, the heat associated with a change in phase is ○ ○ Units of L: J/kg Figure 14.15 Temperature versus Time for a sample of ice to which heat is added continuously ● Temperature varies with time when heat is added continuously to a specimen of ice with an initial temperature below 0C. ● ● A plot of temperature versus time for a sample of ice to which heat is added continuously Problem 14. ● An ice-cube tray contains 0.350 kg of water at 18.0C. How much heat must be removed from the water to cool it to 0.00C and freeze it? Express your answer in joules and in calories. ● Solve:
Calorimetry ● Calorimetry is the science of measuring changes in state variables of a body for the purpose of deriving the heat transfer associated with changes of its state due, for example, physical changes, or phase transitions under specified constraints. Main equation ● The process of exchange heat by objects that reach thermal equilibrium ● Many problems in the homework are about calorimetry: ○ Ex: “what will be the temperature of water if you put 5 kg of ice on top of a 1 kg pack of aluminum heated to 150C Example 14.8 Coffee in a Metal Cup ● This example involves heat flow between a liquid and its container. ● A Turkish restaurant serves coffee in copper mugs (with the inside tin plated to avoid copper poisoning). A waiter fills a cup having a mass of 0.100 kg and initially at 20.0 C with 0.300 kg of coffee that is initially at 70.0C. What is the final temperature after the coffee and the cup attain thermal equilibrium? (assume that coffee has same specific heat as water and there is no heat exchange with the surroundings) ● Solve: ○ Because the coffee loses heat, it has a negative value of Q ■ ○ The heat gained by the copper cup is ■ ○ We equate the sum of these two quantities of heat to zero ■ ■ Solve for T, which ends up being 68.5C
14.7 Heat Transfer
● Conduction — occurs within an object or between objects that are in actual contact with each other.
Example 14. ● A pot with a steel bottom 8.50 mm thick rests on a hot stove. The area of the bottom of the pot is 0.150 m^2. The water inside the pot is at 100.0C and 0.390kg are evaporated every 3.00 min. Find the temperature of the lower surface of the pot, which is in contact with the stove. ● Solve: ○ Given: ■ Thickness: L=8.5mm ■ Area: A=0.15m^ ■ Temperature of the water inside the top: 100C ○ Heat current: ■ ○ Heat conduction ■ Stefan-Boltzmann Law ● Formula ○ ● An object at a temperature T radiates according to the Stefan-Boltzmann law H = AσT^4. ● But the surroundings (at a temperature Ts) are also radiating and the object absorbs the radiation. The net rate of radiation from an object at temperature T with surrounding temperature T(s) is ○ ● If e = 1 the object is called a blockbody… Example 14.14 Radiation from the human body ● If the total surface area of a woman’s body is 1.2m^2 and her skin temperature is 30C, find the total rate of radiation of energy from her body. She also absorbs radiation from her surroundings. If the surroundings are at a temperature of 20C, what is her net rate of heat loss by radiation? The emissivity of the body is very close to unity, irrespective of skin pigmentation. ● Solve:
○ The loss is partly offset by the absorption of radiation, which depends on the temprature of the surroundings. ○ The net rate of radiative energy transfer is ■ Problem 14.59 - Stefan-Boltzmann Law Problem ● By measuring the spectrum of wavelengths of light from our sun, we know that its surface temperature is 5800 K. by measuring the rate at which we receive its energy on earth, we know that it is radiating a total of 3.92 x 10^26 J/s and behaves nearly like an ideal blackbody. Use this information to calculate the diameter of our sun. ● Solve: ○ Given: ■ Surface temperature of sun T=5800K ■ It radiates ■ It behaves like blackbody: e= ○ ○ Example 14.9 Chilling your Soda ● A physics student wants to cool 0.25 kg of lemonade (mostly water) initially at 20°C by adding ice initially at -20°C. How much ice should she add so that the final temperature will be 0°C with all the ice melted? Assume that the heat capacity of the paper container may be neglected. ● Solve: ○
