Physics 141Mechanics Lecture 24 Heat and Temperature Yongli Gao So far we have concentrated on mechanical energy, including potential and kinetic energy. There are other forms of energy and energy may change from one form to another. Heat is a form of energy. It is associated with the microscopic random motion of atoms and molecules. The unit of heat is calorie (cal). 1 cal = J =3.969 x Btu Temperature measures the intensity of the molecular random motion. The unit of temperature is kelvin (K) in so called absolute temperature scale.

Measurement of Temperature The lowest temperature possible is 0 K (absolute zero), at which all the atoms are frozen to minimum vibration. The frozen temperature of water is K = 0 degrees celsius (°C), and the boiling temperature is K = 100 °C, both at the atmosphere pressure (1x10 5 Pa). Celsius scale is internationally used in daily life. In the US, we use Fahrenheit scale in the unit of degrees fahrenheit (°F) in daily life. Room temperature 72.0 °F = °C = K

Thermal Expansion As the temperature of an object increases, the random motions of the molecules also increase. As a result, the average distance between molecules increases, resulting the expansion of the object in all directions. Typically, liquids expand more than solids, and gases much more than liquids. For a solid of length L, the change of length,  L, due to thermal expansion after temperature increase  T is  L=  L  T where  is the coefficient of linear expansion, typically in the order of The volume expension

0th Law of Thermodynamics The zeroth law of thermodynamics states that two systems are in thermal equilibrium when they are of the same temperature T. Thermal equilibrium molecular random motion of the same intensity the same temperature.

Heat Capacity When you put heat  Q into an object, its temperature increases by  T, The coefficient C measures the amount of heat energy necessary the temperature of the object by one temperature unit, and is termed heat capacity. The heat capacity of one unit mass of a material is called the specific heat c of the material, where m is the mass of the object. The typical unit of c is cal/gK, but in SI it is J/kgK. Another common unit for specific heat is called molar specific heat, in which the amount of material is measured by mole (mol) instead of mass l mole = x (atoms or molecules)

Heat Transfer There are three modes of heat transfer, conduction, convection and radiation. Conduction is the transfer of heat by touching or through a heat conductor. Microscopically, it is heat transfer by the collisions of molecules such that the random molecular motions propagate. Convection is the transfer of heat by macroscopic flow of a fluid, such as cooking with a gas heater, drying hair with a hair dryer. Radiation is the transfer of heat by electromagnetic (EM) waves, such as infrared or visible light. We get energy from the sun by radiation heat transfer.

Conduction Suppose we have a heat conductor. When steady, the heat conducted across,  Q, is proportional to the time taken  t, the cross section A, the thermal gradient  T/  x. The heat flow equation for the rate of transfer H where k is the thermal conductivity of the conductor, and the "-" sign means that  Q is from high T to low T. The unit for thermal conductivity k is W/mK, and the value is from 401 (Cu) to (PUT foam). In industry, the insulation is expressed by R=  x/k, where  x is the thickness of the conductor (insulator). In the State of New York, the outer wall of a house must have R≥13.

The First Law of Thermodynamics The first law of thermodynamics states that the heat absorbed by a system in a process,  Q, equals to the sum of internal energy increase,  E, and the work done by the system during the process,  W. This is in fact the conservation of energy.

Entropy In winter if you stand outside and take off your coat, you'll feel cold because heat is dissipated from you to the environment. Why doesn't the net heat flow the other way around? The process above is irreversible. The heat lost to the environment is lost, it cannot come back to you by itself. There are also reversible processes. A reversible process is such that at any moment the system is in equilibrium so that it can go either way. To determine whether a process is irreversible, we need to know entropy, which is a quantity describing the status of a system in a way as energy, temperature, pressure, volume, etc.

The 2nd Thermodynamic Law Entropy is defined as The second thermodynamics law is that for an isolated system in any process, the change of its entropy is non-negative,  S≥0 For example, consider a system with a hot reservoir T h and a cold reservoir at T l. In a contact of the two,  Q goes from the hot reservoir to the cold one but not the other way around.

Statistical Definition of Entropy Entropy is in fact a measurement of disorder. The 2nd law of thermodynamics is in fact stating that by itself, any system prefers more randomness. If W denotes the multiplicity of the system, or the number of possible configurations, entropy of the system can also be defined as S=k B lnW The 3rd law of thermodynamics states that as the temperature goes to zero, the entropy approaches a constant, regardless how it reaches zero. From the statistical point of view, it is the fact that at zero temperature, the system falls into its ground state with a certain number of possible configurations W 0.