Transcript
TEMPERATURE AND HEAT
First it is important to understand the difference between temperature and heat.
Heat is a form of energy whose magnitude depends on the total energy of motion of the molecules within a substance or object.
Temperature is a measure of the average energy of motion of the molecules within a substance or object. It is an indicator of the tendency of a substance to transfer heat energy since heat energy always moves from higher temperature to lower temperature.
The three temperature scales most commonly used are Fahrenheit, Celsius, and Kelvin.
Weather reporting to the public in the U.S. is done using the Fahrenheit scale. Most of the rest of the world uses the Celsius scale. The Kelvin scale is used in scientific work.
Above is a comparison of the Celsius and Fahrenheit scales. To convert between Celsius and Fahrenheit temperatures, we use the formula:
F = (9/5)C + 32
We can substitute a Celsius temperature for C and solve for F or we can substitute a Fahrenheit temperature for F and solve for C.
Example
Find the Celsius temperature that corresponds to 68 degrees Fahrenheit.
The Kelvin scale was developed as a result of studies of gas laws which indicated that the lowest possible temperature for an ideal gas would be -273.15 degrees Celsius. The Kelvin scale simply sets this temperature as zero which then makes Charles's Law relating volume and temperature work.
To convert from Celsius to Kelvin, add 273.15 to the Celsius reading.
A constant-volume gas thermometer is a device which uses the relationship between pressure and temperature to measure temperature.
The bulb containing the gas is immersed in the substance whose temperature is being measured. The right tube of the manometer is adjusted up or down until the left tube mercury level is the same as it was when calibrated. The change in the height difference of the mercury levels can then be used with the combined gas law equation or ideal gas law equation to determine the new temperature.
Thermometers measure temperature by using a thermometric property of the substance composing the thermometer. In a constant volume gas thermometer it is the relationship between temperature and pressure that is used. In a mercury thermometer, the relationship between temperature and linear expansion is used.
The voltage change in a thermocouple can be used to measure a wide range of temperatures. An important medical application involves the detection of infrared radiation, such as the infrared detectors used in the patient's ear. Thermography can show differences in circulation which can be used to diagnose cancers and blood flow problems.
Look in your book on p 341 for an example of the vasoconstriction that occurs when someone smokes a cigarette.
Most objects, when heated, expand. The amount of expansion depends on the original length, the change in temperature and an inherent property of the substance called coefficient of linear expansion. The equations are:
L = Lo + ?Lo
?Lo = ?Lo?T
where ?Lo is the change in the original length, ? is the coefficient of linear expansion, and ?T is the change in temperature.
A table of coefficients of linear and volume expansions on p 342 shows how the amount of expansion can vary from substance to substance.
Example
A concrete sidewalk can buckle when heated if no space is left for linear expansion. If no expansion space is left, the concrete rises to form a right triangle. The amount of rise can be calculated with the Pythagorean theorem. If the coefficient of linear expansion for concrete is 12 x 10-6/C° and the temperature change is 13 C°, find the amount of rise for two 3.00000 m sections of concrete.
A bimetallic strip is made of two layers of metal with different coefficients of linear expansion. Temperature changes may make it bend in either direction depending on whether it is heated or cooled.
These devices are sometimes used as switches to turn heating elements on and off.
A hole in a substance that is heated or cooled will expand or contract the same as if it were filled with the substance around it.
Since each tile expands the same amount, the space between the two middle tiles must expand, too.
Thermal volume expansion is treated the same way as linear expansion with very similar equations.
V = Vo + ?Vo
?Vo = ?Vo?T
? in this case is the coefficient of volume expansion and Vo is the original volume. ? turns out to be about 3? for most solids.
When working problems involving volume expansion of a liquid in a container, you must remember that both the liquid and the container expand. Overflow volume will be reduced by the amount the container expands.
Example
Suppose the steel gas tank in a car is completely filled with 20 gallons of gasoline at 17°C. How many gallons will overflow when the temperature rises to 35°C?
?steel = 36 x 10-6/C°
?gasoline = 950 x 10-6/C°
Water behaves differently from most substances in that it is most dense at about 4 degrees Celsius. As it cools down to 0 degrees Celsius, it expands. When it turns into a solid at 0 degrees Celsius the crystal formation is complete and the increased molecular spacing causes ice to be less dense than water. Since ice floats, bodies of water do not freeze to the bottom. This allows aquatic life to survive in the liquid water at the bottom of the pond.
Here we need to refine the definition of heat energy. It is the energy that is transferred from one object to another because of a temperature difference. Part of the internal energy of one object can be transferred to another object at a lower temperature until they reach the same temperature. If extra energy is added(like on a stove) thermal equilibrium is never reached and heat energy continues to be transferred.
Since heat is a form of energy, the SI unit of heat is the Joule. The other units often used to express heat energy are the calorie, Kilocalorie(Calorie), and the British Thermal Unit(BTU).
The Kilocalorie is used by nutritionists to compare energy values of foods. Unfortunately people confuse the Calorie with the calorie. The calorie was originally defined as the amount of heat energy required to increase the temperature of 1 gram of water 1 Celsius degree. 1Calorie = 1000 calories.
The BTU is the amount of heat energy required to increase the temperature of 1 pound of water 1 Fahrenheit degree. It is still used to compare heating and cooling capacities of heaters, air conditioners, etc.
James Joule investigated the relationship between mechanical energy and heat energy(which were originally thought to be two completely different things). After count Rumford showed that they were in fact related, Joule found that 1 cal = 4.186 j.
This is called the mechanical equivalent of heat.
Adding heat energy to a substance will cause an increase in its temperature or a change in its phase. The equation relating temperature change and heat energy is:
?Q = mc?T
m is the mass of the substance being heated and c is called the specific heat of the substance. Specific heat will vary from substance to substance with the specific heat of water being exceptionally high.
Specific heat capacity of a substance is defined as the amount of energy required to increase the temperature of 1 Kg of the substance 1 Celsius degree.
Example
A resting person has a metabolic rate of 3.0 x 105 j/hr. This person is submerged in a tub with 1200 kg of water at 21°C. If all of the heat generated by the person is absorbed by the water, find the water temperature after half an hour.
When heat transfer causes a change in phase, the amount of heat energy depends on the mass of the substance being changed and an inherent constant. If melting or freezing is the phase change, the constant is the heat of fusion for the substance. If vaporization or condensation is the phase change, the constant is the heat of vaporization for the substance. In the case of melting or freezing, it is the amount of heat energy required to melt one gram of the substance. In the case of vaporization or condensation, it is the amount of heat energy required to vaporize 1 gram of the substance.
The graph shown above is called a heating curve and illustrates the points where phase changes occur.
Calorimetry problems are worked using the idea of conservation of energy. If no heat energy is to enter or leave the system being considered, the amount of heat energy lost by one or more parts of the system must equal the heat energy gained by the other parts of the system. This gives us the equation:
Heat Lost = Heat Gained
This is the beginning point for all calorimetry problems. On the heat lost side we put substances that are cooling off, freezing or condensing. On the heat gained side we put substances that are being heated up, melting or vaporizing. The resulting equation can then be solved for any unknown quantity.
Example
A person eats a container of yogurt which contains 240 Calories.(1 Calorie = 4186 j) How much perspiration must evaporate to get rid of this energy?(Lv = 2.42 x 106 j/kg)
In a closed system, the different phases of matter will reach a state of dynamic equilibrium.
In the diagram above, some water molecules have enough energy to leave the liquid at its surface. This is the evaporation process. When enough water molecules occupy the space above the surface so that the number returning to the liquid state equals the number evaporating, evaporation is no longer apparent and the amount of liquid no longer changes.
The pressure at which this happens is called the equilibrium vapor pressure of the liquid. As the temperature increases, the numerical value of the evp increases. If the evp exceeds the actual pressure above the liquid, the liquid boils.
A pressure cooker uses this principle to attain temperatures above 100 degrees Celsius.
