Gas Behavior and The First Law

Transcription

1 Gas Behavior and The First Law Consider a gas in a cylinder with a movable piston. If the piston is pushed inward by an external force, work is done on the gas, adding energy to the system. The force exerted on the piston by the gas equals the pressure of the gas times the area of the piston: F = PA The work done equals the force exerted by the piston times the distance the piston moves: W = Fd = (PA)d = P V

2 If the gas is being compressed, the change in volume is negative, and the work done is negative. Work done on the system is negative. Negative work increases the energy of the system. If the gas is expanding, positive work is done by the gas on its surroundings, and the internal energy of the gas decreases.

3 An ideal gas is a gas for which the forces between atoms are small enough to be ignored. For an ideal gas, absolute temperature is directly related to the average kinetic energy of the molecules of the system. Most gases behave approximately as ideal gases. If the process is adiabatic, no heat flows into or out of the gas. Even though no heat is added, the temperature of a gas will increase in an adiabatic compression, since the internal energy increases.

4 In an isothermal process, the temperature does not change. The internal energy must be constant. The change in internal energy, U, is zero. If an amount of heat Q is added to the gas, an equal amount of work W will be done by the gas on its surroundings, from U = Q - W. In an isobaric process, the pressure of the gas remains constant. The internal energy increases as the gas is heated, and so does the temperature. The gas also expands, removing some of the internal energy. Experiments determined that the pressure, volume, and absolute temperature of an ideal gas are related by the equation of state: PV = NkT where N is the number of molecules and k is Boltzmann s constant.

5 3E-03 Fire Syringe Compression and rise in air temperature What will happen to the combustible material when the plunger is rapidly pushed down? Can you guess the every-day application of this phenomenon? This system is analogous to the combustion cycle within a diesel engine or any fuel injected engine. RAPID COMPRESSION IS ADIABATIC GIVING RAPID RISE OF AIR TEMPERATURE IN THE CHAMBER WHICH EXCEEDS THE IGNITION TEMPERATURE OF THE FLAMMABLE MATERIAL. 3/7/2011 Physics 214 Fall

6 What process makes a hot-air balloon rise? When gas is heated in a hot-air balloon, the pressure, not the temperature, remains constant. The gas undergoes an isobaric expansion. Since the gas has expanded, the density has decreased. The balloon experiences a buoyant force because the gas inside the balloon is less dense than the surrounding atmosphere.

7 The Flow of Heat There are three basic processes for heat flow: Conduction Convection Radiation

8 In conduction, heat flows through a material when objects at different temperatures are placed in contact with one another.

9 (Conduction Contd.) The rate of heat flow depends on the temperature difference between the objects. It also depends on the thermal conductivity of the materials, a measure of how well the materials conduct heat. For example, a metal block at room temperature will feel colder than a wood block of the exact same temperature. The metal block is a better thermal conductor, so heat flows more readily from your hand into the metal. Since contact with the metal cools your hand more rapidly, the metal feels colder.

10 3B-04 Boiling Water in Cup

11 3B-02 Safety Lamp

12 3D-05 Solar Panel 3D-03 Radiation--Match

13 In radiation, heat energy is transferred by electromagnetic waves. The electromagnetic waves involved in the transfer of heat lie primarily in the infrared portion of the spectrum. Unlike conduction and convection, which both require a medium to travel through, radiation can take place across a vacuum. For example, the evacuated space in a thermos bottle. The radiation is reduced to a minimum by silvering the facing walls of the evacuated space.

14 In convection, heat is transferred by the motion of a fluid containing thermal energy. Convection is the main method of heating a house. It is also the main method heat is lost from buildings.

15 The laws of thermodynamics...are critical to making intelligent choices about energy in today s global economy.

16 How do heat engines work? What determines their efficiency? What Is a Heat Engine?

17 Heat Engines A gasoline engine is a form of a heat engine. Gasoline is mixed with air. A spark ignites the mixture, which burns rapidly. Heat is released from the fuel as it burns. The heat causes the gases in the cylinder to expand, doing work on the piston. The work done on the piston is transferred to the drive shaft and wheels.

18 Heat Engines The wheels push against the road. According to Newton s third law, the road exerts a force on the tires, allowing the car to move forward. Not all the heat from burning fuel is converted to work done in moving the car. The exhaust gases emerging from the tailpipe release heat into the environment. Unused heat is a general feature of heat engines.

19 Heat Engines All heat engines share these main features of operation: Thermal energy (heat) is introduced into the engine. Some of this energy is converted to mechanical work. Some heat (waste heat) is released into the environment at a temperature lower than the input temperature. Q H W Q C

20 3E09, 3E10, 2E12 Engines Stirling Engine Stirling Engine Steam Engine

21 Efficiency is the ratio of the net work done by the engine to the amount of heat that must be supplied to accomplish this work. Efficiency e W Q H

22 A heat engine takes in 1200 J of heat from the high-temperature heat source in each cycle, and does 400 J of work in each cycle. What is the efficiency of this engine? a) 33% b) 40% c) 66% Q H = 1200 J W = 400 J e = W / Q H = (400 J) / (1200 J) = 1/3 = 0.33 = 33%

23 How much heat is released into the environment in each cycle? a) 33 J b) 400 J c) 800 J d) 1200 J Q C = Q H - W = 1200 J J = 800 J

24 Carnot Engine The efficiency of a typical automobile engine is less than 30%. This seems to be wasting a lot of energy. What is the best efficiency we could achieve? What factors determine efficiency? In analogy to water wheels, Carnot reasoned that the greatest efficiency of a heat engine would be obtained by taking all the input heat at a single high temperature and releasing all the unused heat at a single low temperature.

25 Carnot Engine and Carnot Cycle Carnot also reasoned that the processes should occur without undue turbulence. The engine is completely reversible: it can be turned around and run the other way at any point in the cycle, because it is always near equilibrium. This is Carnot s ideal engine. The cycle devised by Carnot that an ideal engine would have to follow is called a Carnot cycle. An (ideal, not real) engine following this cycle is called a Carnot engine.

26 1. Heat flows into cylinder at temperature T H. The fluid expands isothermally and does work on the piston. 2. The fluid continues to expand, adiabatically. 3. Work is done by the piston on the fluid, which undergoes an isothermal compression. 4. The fluid returns to its initial condition by an adiabatic compression.

27 Carnot Efficiency The efficiency of Carnot s ideal engine is called the Carnot efficiency and is given by: e C T H T C T H This is the maximum efficiency possible for any engine taking in heat from a reservoir at absolute temperature T H and releasing heat to a reservoir at temperature T C. Even Carnot s ideal engine is less than 100% efficient.

28 A steam turbine takes in steam at a temperature of 400 C and releases steam to the condenser at a temperature of 120 C. What is the Carnot efficiency for this engine? a) 30% b) 41.6% c) 58.4% d) 70% T H = 400 C = 673 K T C = 120 C = 393 K e C = (T H - T C ) / T H = (673 K K) / (673 K) = 280 K / 673 K = = 41.6%

29 If the turbine takes in 500 kj of heat in each cycle, what is the maximum amount of work that could be generated by the turbine in each cycle? a) 0.83 J b) kj c) 28 kj d) 208 kj Q H = 500 kj e = W / Q H, so W = e Q H = (0.416)(500 kj) = 208 kj