AP Physics B: Lecture #21 Second Law of Thermodynamics “Heat will not flow spontaneously from a colder body to a warmer body AND heat energy cannot be transformed completely into mechanical work.” The bottom line: 1)Heat always flows from a hot body to a cold body 2)Nothing is 100% efficient

When a substance undergoes a temperature change, it changes in size. Linear Expansion:The increase in any one dimension of a solid. The length L 0 of an object changes by an amount ΔL when its temp. changes by an amount ΔT. ΔL = αL 0 ΔT Coefficient of Linear Expansion Unit: (1/C o or C o-1 ) ΔL is also proportional to L 0.

Bridge expansion joint. In August the teeth will mesh together. This track was laid in February; the picture was taken in August. Concrete patio buckles. No expansion gap was included.

When a substance undergoes a temperature change, its volume changes. Volume Expansion: The volume V 0 of an object changes by an amount ΔV when its temp. changes by an amount ΔT. ΔV = βV 0 ΔT Coefficient of Volume Expansion Unit: (1/C o or C o-1 ) ΔV is also proportional to V 0. Atoms have small amplitude of vibration at low temperature. At a higher temperature, atoms have a larger amplitude of vibration.

The amount of heat required to change the temperature of a given substance is directly related to the mass of the substance, the amount of temperature change, and the specific heat capacity of the substance. Q = cmΔT Heat Specific Heat Capacity mass Change in Temp. specific heat capacity depends on the nature of the material. Units of Heat: Joule (J) calorie (cal), kilocalorie (kcal) = 1 Calorie (Cal) British Thermal Unit (Btu) *Amount of heat needed to raise the temperature of one pound of water by 1 0 F. 1 kcal = 4184 joules

Latent Heat (L):The heat per kilogram that must be added or removed when a substance changes from one phase to another at a constant temperature. Latent heat of fusion (L f ) - Change between solid and liquid phases Latent heat of vaporization (L v ) – Change between liquid and gas phases Latent heat of sublimation (L s ) – Change between solid and gas phases

Convection:The process in which heat is carried from place to place by the bulk movement of a fluid. The fluid flow carries along heat and is called a convection current. It is the transfer of heat by the actual movement of the warmed matter. Heat leaves the coffee cup as the currents of steam and air rise.

Conduction is the transfer of energy through matter from particle to particle. It is the transfer and distribution of heat energy from atom to atom within a substance. Thermal Conductors: Thermal Insulators: Materials that conduct heat well. Materials that conduct heat poorly. Aluminum, copper, gold, silver Wood, glass, most plastics

Q = (kA ΔT)t L Heat Flow HotCold L Heat Conducted Time Constant (Thermal Conductivity) Cross- Sectional Area Length Temperature difference between the ends of the material. Unit for k: J. m/(s. m 2. C o ) or W/m. C o

Radiation:The process in which energy is transferred by means of electromagnetic waves. Blackbody: An object that absorbs all the electromagnetic waves falling on it.

Engines Heat flows from a HOT reservoir to a COLD reservoir Q H = remove from, absorbs = hot Q C = exhausts to, expels = cold

Engine Efficiency In order to determine the thermal efficiency of an engine you have to look at how much ENERGY you get OUT based on how much you energy you take IN. In other words:

Rates of Energy Usage Sometimes it is useful to express the energy usage of an engine as a RATE. For example: The RATE at which heat is absorbed! The RATE at which heat is expelled. The RATE at which WORK is DONE

Efficiency in terms of rates

Is there an IDEAL engine model? Our goal is to figure out just how efficient such a heat engine can be: what’s the most work we can possibly get for a given amount of fuel? The efficiency question was first posed—and solved—by Sadi Carnot in 1820, not long after steam engines had become efficient enough to begin replacing water wheels, at that time the main power sources for industry. Not surprisingly, perhaps, Carnot visualized the heat engine as a kind of water wheel in which heat (the “fluid”) dropped from a high temperature to a low temperature, losing “potential energy” which the engine turned into work done, just like a water wheel.

Carnot Efficiency Carnot believed that there was an absolute zero of temperature, from which he figured out that on being cooled to absolute zero, the fluid would give up all its heat energy. Therefore, if it falls only half way to absolute zero from its beginning temperature, it will give up half its heat, and an engine taking in heat at T and shedding it at ½T will be utilizing half the possible heat, and be 50% efficient. Picture a water wheel that takes in water at the top of a waterfall, but lets it out halfway down. So, the efficiency of an ideal engine operating between two temperatures will be equal to the fraction of the temperature drop towards absolute zero that the heat undergoes.

Carnot Efficiency Carnot temperatures must be expressed in KELVIN!!!!!! The Carnot model has 4 parts An Isothermal Expansion An Adiabatic Expansion An Isothermal Compression An Adiabatic Compression The PV diagram in a way shows us that the ratio of the heats are symbolic to the ratio of the 2 temperatures