MCAT Physics and Math - Thermodynamics

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Thermodynamics

the study of the flow of energy in the universe, as that flow relates to work, heat, entropy, and the different forms of energy

Classical thermodynamics

observations that can be made at the macroscopic level, such as measurements of temperature, pressure, volume, and work

zeroth law of thermodynamics

when one object is in thermal equilibrium with another object and the second object is in thermal equilibrium with a third object, then the first and third object are also in thermal equilibrium; no net heat flow

If a = b and b = c, then a = c

temperature

colloquial: how hot or cold something is

molecular: is proportional to the average kinetic energy of the particles that make up the substance

macroscopic: difference between two objects determines the direction of heat flow, from high to low

Heat

transfer of thermal energy from a hotter object with higher temperature (energy) to a colder object with lower temperature

thermal equilibrium

no net heat flows between two objects in thermal contact; temperatures are equal

Celsius (°C)

0° and 100° define the freezing and boiling temperatures of water

Fahrenheit (°F)

32° and 212° define the freezing and boiling temperatures of water

Kelvin (K)

most commonly used for scientific measurements; one of the seven SI base units; freezing point of water as 273.15 K; a change of one degree Celsius equals a change of one unit kelvin

absolute zero (0K)

the theoretical temperature at which there is no thermal energy

third law of thermodynamics

the entropy of a perfectly organized crystal at absolute zero is zero

Fahrenheit-Celsius conversion

180 degrees between water’s phase changes on the Fahrenheit scale, rather than 100 degrees as on both the Celsius and the Kelvin scales

Thermal Expansion

A change in the temperature of most substances results in a change in their length/volume

coefficient of linear expansion (α)

constant that characterizes how a specific material’s length changes as the temperature changes; usually has units of K^–1

linear thermal expansion

ΔL = αLΔT

where ΔL is the change in length, α is the coefficient of linear expansion, L is the original length, and ΔT is the change in temperature

volumetric thermal expansion

ΔV = βVΔT

where ΔV is the change in volume, β is the coefficient of volumetric expansion, V is the original volume, and ΔT is the change in temperature

coefficient of volumetric expansion

constant that characterizes how a specific material’s volume changes as the temperature changes; three times the coefficient of linear expansion for the same material (β = 3α)

system

the portion of the universe that we are interested in observing or manipulating

surroundings

the rest of the universe, excluding the system

Isolated systems

not capable of exchanging energy or matter with their surroundings; ΔE = 0

ex. bomb calorimeter (approximate), whole universe

Closed systems

capable of exchanging energy, but not matter, with the surroundings

ex. gases in vessels with movable pistons

Open systems

can exchange both matter and energy with the environment

State functions

thermodynamic properties that are a function of only the current equilibrium state of a system; path independent

ex. include pressure (P), density (ρ), temperature (T), volume (V), enthalpy (H), internal energy (U), Gibbs free energy (G), and entropy (S)

process functions

describe the path taken to get to from one state to another

ex. work, heat

first law of thermodynamics

the change in the total internal energy of a system is equal to the amount of energy transferred in the form of heat to the system, minus the amount of energy transferred from the system in the form of work; energy conservation

ΔU = Q − W
where ΔU is the change in the system’s internal energy, Q is the energy transferred into the system as heat, and W is the work done by the system.

work

as the process by which energy is transferred as the result of force being applied through some distance

second law of thermodynamics

objects in thermal contact and not in thermal equilibrium will exchange heat energy such that the object with a higher temperature will give off heat energy to the object with a lower temperature until both objects have the same temperature at thermal equilibrium

that energy spontaneously disperses from being localized to becoming spread out if it is not hindered from doing so

ΔS_universe = ΔS_system + ΔS_surroundings > 0

Heat

the process by which a quantity of energy is transferred between two objects as a result of a difference in temperature

measured in Joules (J), calories (cal), nutritional Calorie (Cal = kcal), British Thermal Unit (BTU)

heat unit conversions

1 Cal ≡ 10³ cal = 4184 J = 3.97 BTU

Conduction

direct transfer of energy from molecule to molecule through molecular collisions; direct physical contact

ex.

Metals - good (sea of electrons facilitates rapid energy transfer)

Gases - poor (space btwn individual molecules)

Convection

transfer of heat by the physical motion of a fluid over a material; flow

ex. convection oven

Radiation

transfer of energy by electromagnetic waves; can transfer through a vacuum

ex. Sun, radiant ovens

specific heat (c)

the amount of heat energy required to raise one gram of a substance by one degree Celsius or one unit kelvin; changes with phase

ex. water - 1 cal/g*K = 4.184 J/g*K

heat and temperature equation

q=mcΔT

where m is the mass, c is the specific heat of the substance, and ΔT is the change in temperature (in Celsius or kelvins).

heat of transformation/latent heat

When a substance is undergoing a phase change, such as from solid to liquid or liquid to gas, the heat that is added or removed from the system does not result in a change in temperature.

q = mL

fusion/melting

solid to liquid

freezing/solidification

liquid to solid

boiling/evaporation/vaporisation

liquid to gas

condensation

gas to liquid

sublimation

solid to gas

deposition

gas to solid

heat of fusion

corresponding heat of transformation to fusion/melting

heat of vaporisation

corresponding heat of transformation to

boiling/evaporation/vaporisation

isothermal

constant temperature, and therefore no change in internal energy

ΔU = 0

Q = W

adiabatic

no heat exchange

Q = 0

ΔU = −W

isovolumetric/isochoric

no change in volume, and therefore no work accomplished

W = 0

ΔU = Q

Isobaric

occur at a constant pressure

closed-loop thermodynamic process

Because the work on a P–V graph is simply the area under the curve, the work done in this closed-loop process is the area inside the loop

Entropy

measure of the spontaneous dispersal of energy at a specific temperature: how much energy is spread out, or how widely spread out energy becomes in a process; number of microstates; more freedom of movement

units usually J/mol*K

Change in entropy

ΔS = Q_rev/T

where ΔS is the change in entropy, Q_rev is the heat that is gained or lost in a reversible process, and T is the temperature in kelvin

time’s arrow

second law; because there is a unidirectional limitation on the movement of energy by which we recognize before and after or new and old

natural process

a process existing in or produced by nature (rather than by deliberate intent)

irreversible

a process that is not reversible

reversible

a process, involving a system and its surroundings, whose direction can be reversed by infinitesimal changes in some properties of the surroundings, such as pressure or temperature; thermodynamic equilibrium

unnatural process

process that woukd not be observed in nature spontaneously