Units of Chapter 18 - San Francisco State Universitywman/phy111hw/lecture notes...Units of Chapter 18 • The First Law of Thermodynamics • Thermal Processes • Specific Heats for

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.


If a system does work on the external world, and no heat is added, its internal energy decreases.


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


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


If the volume stays constant, nothing moves and no work is done.


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.


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.


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.


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.


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!


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.


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:


• 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:


• 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


Units of Chapter 18

The following is not required

• Entropy

• Order, Disorder, and Entropy• Order, Disorder, and Entropy

• The Third Law of Thermodynamics

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Units of Chapter 18 - San Francisco State Universitywman/phy111hw/lecture notes...Units of Chapter 18 • The First Law of Thermodynamics • Thermal Processes • Specific Heats for