Upload
truongxuyen
View
214
Download
1
Embed Size (px)
Citation preview
Units of Chapter 18
• The First Law of Thermodynamics
• Thermal Processes
• Specific Heats for an Ideal Gas: Constant Pressure, Constant VolumePressure, Constant Volume
• The Second Law of Thermodynamics
• Heat Engines and cooling system
•Refrigerators, Air Conditioners, and Heat Pumps
17-2 Kinetic Theory for ideal gas
The kinetic theory relates microscopic quantities (position, velocity) to macroscopic ones (pressure, temperature). Assumptions:
• N identical molecules of mass m are inside a container of volume V; each acts as a point container of volume V; each acts as a point
particle.
• Molecules move randomly and always obey Newton’s laws.
• Collisions with other molecules and with the walls are elastic.
17-2 Kinetic Theory
Pressure is the result of collisions between the gas molecules and the walls of the container.
It depends on the mass and speed of the It depends on the mass and speed of the molecules, and on the container size:
Therefore, the pressure in a gas is proportional to the average kinetic energy of the random thermal motion of its molecules, Thermal energy.
17-2 Kinetic Theory
Not all molecules in a gas will have the same speed; their speeds are represented by the Maxwell distribution, and depend on the temperature and mass of the molecules.
17-2 Kinetic Theory
The average kinetic energy of the random thermal motion of EACH gas molecule = 3/2 kT
17-2 Kinetic Theory
The internal energy of an ideal gas is the sum of the kinetic energies of all its molecules. In the case where each molecule consists of a single atom, this may be written:
18-2 The First Law of Thermodynamics
The first law of thermodynamics is a statement of the conservation of energy.
If a system’s volume is constant, and heat is added, its internal energy increases.
18-2 The First Law of Thermodynamics
If a system does work on the external world, and no heat is added, its internal energy decreases.
18-2 The First Law of Thermodynamics
Combining these gives the first law of
thermodynamics. The change in a system’s
internal energy is related to the heat Q and the
work W as follows:
It is vital to keep track of the signs of Q and W.It is vital to keep track of the signs of Q and W.
Expand
18-2 The First Law of Thermodynamics
The internal energy of the system depends only on its temperature. When the idea gas system returns to previous temperature, its internal energy returns to its initial level.
The work done and the heat added, however, depend on the details of the process involved.
18-3 Thermal Processes
Work done by an expanding gas, constant pressure:
W=PVf - PVi= Nk (Tf-Ti) =nR∆∆∆∆T
18-3 Thermal Processes
A summary of the different types of thermal processes:
At constant pressure,
For a constant-volume process,
=∆U
=nR∆T
=∆U+ nR∆T
18-4 Specific Heats for an Ideal Gas: Constant Pressure, Constant Volume
Although this calculation was done for an ideal, monatomic gas, it works well for real gases.
HW help:
An ideal gas is taken through the three processes shown in figure below.
∆∆∆∆U=Q-W
when Volume of gas do not change, Work done by the gas is ____.
It is also important to notice that from state Ato B to C3 back to Atotal change in internal thermal energy is deltaU(1 to 2) +deltaU(2 to 3)+ deltaU(3 to 1)and that is equal to ____, because after 3 steps it goes back to initial P,V and T.
A 5.0 kg block of ice at -1.5°C slides on a horizontal surface with a coefficient of kinetic friction equal to 0.060. The initial speed of the block is 6.3 m/s and its final speed is 5.5 m/s. Assuming that all the energy dissipated by kinetic friction goes into melting a small mass m of the ice, and that the rest of the ice block remains at -1.5°C, determine the value of m.
1, Since the mass lost in melting is too small comparing to 5kg, Assume the mass of the ice block is still 5kg at the end. 2, Assume that the temperature of the rest of the ice didn’t increase, all heat generated was used by the very thin layer of melted ice.
Ef= Ei+WncIf you know how much was the energy (total KE and PE) change, you know how much work was done by friction here, right?. So, can you easily find the work done by friction by looking at mechanical Energy change? (question 6b in midterm 2).
Once we get the work done by friction, its absolute value is equal to the total heat absorbed by the small amount of melted ice, (m_melt). You will need specific heat of ice c_ice = 2030 J per kg per degree. And latent heat for fusion: Lf = 33.5 *10^4 J/kg , to find that mass
18-5 The Second Law of Thermodynamics
When objects of different temperatures are brought
into thermal contact, the spontaneous flow of heat
that results is always from the high temperature
object to the low temperature object. Spontaneous
heat flow never proceeds in the reverse direction.
A heat engine is a device that A heat engine is a device that converts heat into work. A classic example is the steam engine. Fuel heats the water; the vapor expands and does work against the piston; the vapor condenses back into water again and the cycle repeats.
18-6 Heat Engines and the Carnot Cycle
All heat engines have:
• a high-temperature reservoir
• a low-temperature reservoir
• a cyclical engine
An amount of heat Qh is supplied from
the hot reservoir to the engine during the hot reservoir to the engine during each cycle. Of that heat, some appears as work, and the rest, Qc, is given off
as waste heat to the cold reservoir.
The efficiency is the fraction of the heat supplied to the engine that appears as work.
18-6 Heat Engines and the Carnot Cycle
In order for the engine to run, there must In order for the engine to run, there must be a temperature difference; otherwise heat will not be transferred.
18-6 Heat Engines and the Carnot Cycle
The maximum work a heat engine can do is then:
If the two reservoirs are at the same If the two reservoirs are at the same temperature, the efficiency is zero; the smaller the ratio of the cold temperature to the hot temperature, the closer the efficiency will be to 1.
18-7 Refrigerators, Air Conditioners, and Heat Pumps
While heat will flow spontaneously only from a higher temperature to a lower one, it can be made to flow the other way if work is done on the system. Refrigerators, air conditioners, the system. Refrigerators, air conditioners, and heat pumps all use work to transfer heat from a cold object to a hot object.
18-7 Refrigerators, Air Conditioners, and Heat Pumps
If we compare the heat engine and the refrigerator, we see that the refrigerator is basically a heat engine running engine running backwards – it uses work to extract heat from the cold
reservoir (the inside of the refrigerator) and exhausts to the kitchen. Note that- more heat is exhausted to the kitchen than is removed from the refrigerator.
18-7 Refrigerators, Air Conditioners, and Heat Pumps
An ideal refrigerator would remove the most heat from the interior while requiring the smallest amount of work. This ratio is called the coefficient of performance, COP:
Typical refrigerators have COP values between 2 and 6. Bigger is better!
18-7 Refrigerators, Air Conditioners, and Heat Pumps
An air conditioner is essentially identical to a refrigerator; the cold reservoir is the interior of the house or other space being cooled, and the hot reservoir is outdoors. the hot reservoir is outdoors. Exhausting an air conditioner within the house will result in the house becoming warmer, just as keeping the refrigerator door open will result in the kitchen becoming warmer.
18-7 Refrigerators, Air Conditioners, and Heat Pumps
In an ideal heat pump with two operating temperatures (cold and hot), the Carnot relationship holds; the work needed to add heat Qh to a room is:
The COP for a heat pump:
Summary of Chapter 17
• An ideal gas is one in which interactions between molecules are ignored.
• Equation of state for an ideal gas:
• Boltzmann’s constant:
• Universal gas constant:• Universal gas constant:
• Equation of state again:
• Number of molecules in a mole is Avogadro’s number:
Summary of Chapter 17
• Molecular mass:
• Constant T:
• Constant P:
• Kinetic theory: gas consists of large • Kinetic theory: gas consists of large number of point like molecules
• Pressure is a result of molecular collisions with container walls
• Internal energy of monatomic gas:
Summary of Chapter 17
• Most common phases of matter: solid, liquid, gas
• When phases are in equilibrium, the number of molecules in each is constant
• Evaporation occurs when molecules in liquid move fast enough to escape into gas phase
• Latent heat: amount of heat required to transform from one phase to another
• Latent heat of fusion: melting or freezing