Internal Energy • The internal energy of an object or physical system is the sum of the kinetic and potential energies of all the constituent atoms or molecules of the object or system • Potential energy arises from attractive/repulsive forces between atoms or molecules or from interaction with external influences • Relative importance of PE and KE depends on phase of matter: Solid (KE+PE) Liquid Ideal Gas (KE only)

Heat Heat is transfer of energy between objects as a result of a temperature difference between them Temperature of an object is associated with the kinetic energy of the constituent atoms/molecules Motion of atoms/molecules is random Heat is energy transfer associated with random motion

Kinetic energy k is Boltzman’s constant (1.38 x 10–23 J•K–1) *Note - this is the KE associated with the motion of a molecule (atom) relative to the object KE of all atoms → KE = NkT Where N = number of molecules (atoms)

Postulates of Kinetic Molecular Theory Large number of molecules (N) moving in random directions and a variety of speeds. They are far apart, with the separation distances being vast compared to the diameter of each particle. Molecules obey laws of mechanics. They attract each other, but we ignore this since the speeds and KE are huge. Collisions with each other and container walls are assumed to be perfectly elastic. Conservation of p and KE. * The higher the temperature the faster the molecules move. The particles vary in speed, so we can only measure an average. Half will be going faster and half slower than the average. Average KE is a reflects this speed.

1.39 x 10-25 kg The atomic masses on the periodic table represent: Kemistree Review: The atomic masses on the periodic table represent: The molar mass of the element in grams/mol Avogadro's number = 6.02 x 1023 mol-1 Example: what is the mass of a Krypton atom in kg? Molar mass of Krypton is 83.80 g/mol 83.80 g 1 mol 1.0 kg x x = mol 1000 g 6.02 x 10 23 1.39 x 10-25 kg

Calculate the average kinetic energy of the CH4 molecules in a sample of CH4 gas at 253 K. KE = kT KE = (1.38 x 10-23) (253) KE = 5.24 x 10-21 J What is the average speed of the CH4 molecules? Molar mass of methane is 16.043 g/mol 16.043 g 1 mol 1.0 kg x x = 2.66 x 10-26 kg mol 6.02 x 10 23 1000 g v = 628 m/s KE = mv2 5.24 x 10-21 = (2.66 x 10-26) v2

As the molecules vibrate with larger energy, they spread out Thermal expansion In addition to causing a temperature or phase change, the transfer of heat to a substance also causes it to expand. Why? As the molecules vibrate with larger energy, they spread out Almost all forms of matter expand when heated and contract when cooled. The one important exception is what substance? H2O Architects and engineers must be sure to consider thermal expansions in their designs. Dentists must also be aware of thermal expansion.

NOTE: 3α = β (given volume is length in three dimensions) Linear Expansion ΔL = L α ΔT Where: ΔL = change in length L = original length α = coefficient of linear expansion ΔT = temperature change Volume Expansion ΔV = V β ΔT Where: ΔV = change in volume V = original volume β = coefficient of volume expansion ΔT = temperature change NOTE: 3α = β (given volume is length in three dimensions)

ΔL = L α ΔT (0.8)= L (16.5 x 10-6) (160) L = 303 m ΔL = 1.73 x 10-3 cm A copper bar changes in length by 0.8 meters with a 160 Celsius degree change in temperature. What is the bar’s original length? (α = 16.5 x 10-6 C°-1 for Cu) ΔL = L α ΔT (0.8)= L (16.5 x 10-6) (160) L = 303 m A brass washer has a circumference of 16 cm at 15°C, by how much will its diameter increase when the temperature reaches a of 33°C. (α = 18.9 x 10-6 C°-1 for brass) Circumference = 2πr r = 2.55 cm ∴ d = 5.10 cm (original length) 16 = 2πr ΔL= 5.10 (18.9 x 10-6) (18) ΔL = 1.73 x 10-3 cm

First, find the expansion of the mercury A glass flask whose volume is exactly 1000 cm3 at 0 °C is filled level of mercury ( β =1.82 x 10-4 C°-1) at this temperature. When the flask and mercury are heated to 100 °C, 15.2cm3 of mercury overflow. Find the coefficient of linear expansion of the glass flask. First, find the expansion of the mercury ΔV = V β ΔT ΔV = 1000 (1.82 x 10-4) (100) ΔV = 18.2 cm3 ∴ glass expanded by 18.2 – 15.2 = 3.0 cm3 β = 3.0 x 10-5 C°-1 3.0 = 1000 (β) (100) Thus α = 1.0 x 10-5 C°-1