Chapter 13 Temperature and Kinetic Theory

*What evidence came to light in the early 1800’s that atoms exist?

What is the mass of ¹²C in atomic mass units (u)? Atomic mass units will be very important next semester in the study of nuclear energy.

What is Brownian motion? What can be learned about atoms from Brownian motion?

What is the approximate size of a neutral atom?

What would the universe be like if

a) the electrical force between atoms did not become repulsive?

b) the electrical force between atoms was not attractive?

c) …

Calculate the average distance between molecules of air at room temperature at 1 atmosphere of pressure. density = 1.29 kg/m³ . Assume the air is all N₂

How would you revise Figure 13-2 to make it better represent the microscopic view of materials?

13.2 Temperature and Thermometers

*Hot and cold are common but very unscientific terms which are used to describe the temperature of a person or object. A thermometer is a device that makes a measurement of temperature and thus puts this quantity on a firm scientific footing.

The temperature of an object can be measured because temperature is related to the following: 1) length of a solid, 2) volume of an object or liquid or gas, 3) gas pressure, 4) electrical resistance, 5) emission of light from a solid, liquid or gas, and 6) transmission of light through a material.

To make a thermometer useful it must be calibrated. The common calibration temperatures on the Celsius scale are 0^o C (freezing point of water) and 100^o C (boiling point of water), both at a pressure of 1 atmosphere. In the calibration process the thermometer is allowed to achieve thermal equilibrium with an object which has a temperature of one of the calibration conditions. The symbol C indicates that the Celsius temperature scale is being used. The Fahrenheit scale has values of 32^o F and 212^o F for the freezing and boiling points.

If one knows the Celsius temperature how can the Fahrenheit temperature be computed?

Since expansion rates of materials are not linear, a constant-volume gas thermometer (page 387) is used for precise temperature measurements. In a future section we will find that pressure, volume and temperature are related variables.

* Thermal Equilibrium Two objects are in thermal equilibrium when they have the same temperature. Thermal equilibrium can be established by leaving objects in contact for a sufficient length of time. Thermal equilibrium can also be established when objects are not in contact (see the discussion of radiation in section 14.9).

If two objects are in thermal equilibrium will one object gain energy while the other object looses energy?

*The Zeroth Law of Thermodynamics states that two objects, each in thermal equilibrium with a third object, are in thermal equilibrium with each other.

i.e if T_A = T_C and T_B = T_C then T_A = T_B

When a solid experiences a rise in temperature it expands. This is due to the increased vibration (KE _cm ) of the molecules. They effectively occupy more space when they are vibrating at larger amplitudes. The change in length is calculated with

D L = a L_o D T a is the coefficient of linear expansion. See Table 13.1

Volume Expansion of Solids and Liquids

The motion of molecules is a three-dimensional effect. Thus, objects expand in all three dimensions when the temperature of the object increases. The equation that models this expansion is

D V = b V_o D T

b is the coefficient of volume expansion. It is approximately equal to 3 * a

Why should you put "antifreeze" in the radiator of your car?

skip the details of 13.6 Thermal Stresses

What happens to the volume of a toy balloon when you press on it with both hands?

If the temperature and number of particles in a gas system are constant then Boyle’s Law holds: PV = constant It is often used as P₁V₁ = P₂V₂

The pressure in a closed system is 2 atmospheres. The initial volume is 3 liters. If the volume is changed to 2 liters, while holding the temperature constant, what is the new value of the pressure?

Volume Expansion of Gases

If a gas is in a container that is flexible (i.e. the container does not have a fixed volume) then the volume of the gas will increase when the temperature is increased (given that the pressure is constant). For normal temperatures this is a linear relationship. The linear relationship does not hold when the temperature is near the vaporization temperature of the gas (i.e. when it is about to condense into a liquid). It also does not hold when the temperature reaches a level where either the molecules dissociate or the atoms become ionized. On a volume vs. temperature graph, different gases (e.g. carbon dioxide, nitrogen, oxygen …) have different slope lines but the extrapolation of the lines all intersect the temperature axis near -273^o C, absolute zero.

The third temperature scale that we will use is the Kelvin temperature scale. This is an absolute temperature scale in which 0 Kelvin occurs at approximately -273 Celsius. At this temperature, absolute zero, the KE of the center of mass of a molecule is zero.

A change in temperature of 1 Kelvin is also a change of 1 degree Celsius. Only the zero point differs for these two scales. Some equations require that the temperature be expressed in Kelvin units.

Charles Law

If the pressure and number of particles in a gas system are constant then V/T = constant.

Gay-Lussac’s Law

If the volume and number of particles are constant then P a T, or P/T = constant.

An Ideal Gas has two main characteristics: 1) there are no long range forces between the molecules, 2) the molecules occupy zero volume.

The various named gas laws previously discussed in the text are contained in the Ideal Gas Law: PV = nRT Note that T is the Kelvin temperature. n represents the number of moles of gas. P is measured in Pascals. V is measured in m³. R is the universal gas constant 8.315 J/ mole/K. The Ideal Gas Law is an equation of state. The pressure, volume, number of moles and temperature are state variables.

The number of moles in a pure sample can be computed by dividing the mass of the sample by the molecular weight. How many moles are present in 36 grams of CO₂?

One mole of gas will occupy 22.4 liters when the Temperature is 273.15K and the pressure is 101 kPa.

What questions do you have on the examples in the text?

In class we will work problems 35 and 41.

Consider PV = nRT . TRUE or FALSE R has a different value for different gases (H vs. He for example).

Avogadro’s Hypothesis

Equal volumes of gas at the same pressure and temperature contain equal numbers of molecules.

n = N/N_A The number of particles, N, in one mole of a substance is 6.02 X 10²³. This is Avogadro’s number, . N_A

The Ideal Gas Law can also be written as PV = NkT, where k is Boltzmann’s constant and N is the number of particles. k = 1.3807 x 10^-23 JK^-1

The gas in our lab room consists of a great number of particles that are moving in random motion (random directions).

Describe any forces that act on the particles of an ideal gas.

The analysis of the motion and collisions yields the following equation:

(13.7) PV = (2/3)N( ½ mv²) ½ mv² is the average KE of the molecules

Recall the Ideal Gas Law PV = nRT. We now set the right sides of the two equations equal to each other, divide by Avagadro’s number and find:

(13.8) KE = (3/2) kT k = 1.3807 x 10^-23 JK^-1

* The Kelvin temperature of an Ideal Gas is directly proportional to the average KE of the center of mass of the molecules.

The gas molecules in any sample of gas above 0 Kelvin have a distribution of speeds from near 0 m/s up to very large values. A characteristic velocity of a gas is its root-mean-square speed,

Calculate the rms velocity for a carbon dioxide molecule in this classroom.

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