Chapter 1 Definitions - An Introduction to Thermal Physics, Schroeder

temperature

1. What you measure with a thermometer

2. the thing that's the same for two objects, after they've been in contact long enough

3. a measure of the tendency of an object to spontaneously give up energy to its surroundings. When two objects are in thermal contact, the one that tends to spontaneously lose energy is at the higher temperature

operational definition

a statement of the procedures used to define research variables (like temperature)

theoretical definition

assigns a meaning to a word by suggesting a theory that characterizes some tendency of the thing in question

thermal equilibrium

The state of two or more objects in thermal contact after reaching common temperature

relaxation time

the time it takes for a system to reach (thermal) equilibrium

diffusive equilibrium

when molecules of two substances in a mixture are free to move around but no longer have any tendency to move one way or another

mechanical equilibrium

when large-scale mechanical motions (expansion of a balloon) can take place but no longer do

absolute zero

the lowest possible temperature state, the zero-point of the absolute temperature scale

Kelvin

SI unit for temperature, which is the same size as a degree Celsius, but with zero K being absolute zero

ideal gas law (mole Equation)

PV = nR*T

P - pressure

V - volume

n - moles of gas

R - universal gas constant

T - temperature in K

ideal gas law (particle equation)

PV = Nk*T

P - pressure

V - volume

N - number of particles gas

k - Boltzmann's constant

T - temperature in K

ideal gas law (definition)

the mathematical relationship among pressure, volume, temperature, and the number of moles of a gas, valid in the limit of low density gas

average translational kinetic energy

K_trans = 3/2kT

k = Boltzmann's

T = temperature

root mean square thermal velocity

v_rms = sqrt(3kT/m)

k = Boltzmann's

m = mass

equipartition theorem (definition)

At temperature T, the average energy of any quadratic degree of freedom is 1/2kT

k = Boltzmann's

T = temperature

degree of freedom

each of a number of independently variable factors affecting the range of states in which a system may exist, in particular any of the directions in which independent motion can occur

total thermal energy

U_therm = Nf1/2kT

N = number of particles

f = degrees of freedom

k = Boltzmann's

T = temperature

energy

A fundamental entity of nature that is transferred between parts of a system in the production of physical change within the system and usually regarded as the capacity for doing work

conservation of energy

while energy can be converted from one form to another, the total energy of the universe never changes

heat

any spontaneous flow of energy from one object to another, caused by a difference in temperature between the objects (passive)

work

non-spontaneous transfer of energy into or out of a system that is not heat (active)

first law of thermodynamics (equation)

{Delta}U = Q+W

{Delta}U - change in energy

Q - heat added

W - work done

calorie

the amount of heat required to raise the temperature of a gram of water by 1 degree C

1 cal = 4.186 J

conduction

the transfer of heat by molecular contact

convection

the bulk motion of a gas or a liquid, usually driven by the tendency of warmer material to expand and rise in a gravitational field

radiation

the emission of electromagnetic waves, mostly infrared for objects at room temperature but including visible light for hotter objects

quasistatic process

a process carried out so slowly that the system has time to continually equilibrate

quasistatic work

W = {int, V_i, V_f} -P(V) dV

V_i - initial volume

V_f - final volume

P(V) - pressure fxn of volume

isothermal compression (definition)

compression of a system which is so slow that the temperature of the gas does not change ({Delta}T = 0)

adiabatic compression (definition)

compression of a system that is so fast that no heat escapes from the system (Q = 0)

isotherm

a line at a given constant temperature that shows the pressure versus volume relationship of a gas

isothermal work

W = NkT*ln(V_i/V_f)

N - number molecules

k - Boltzmann's

V_i - initial volume

V_f - final volume

isothermal work tendencies

- heat input will be minus the work done (T=constant, {Delta}U proportional to {Delta}T)

- work (+) for compression, (-) for expansion

- heat (-) for compression, (+) for expansion

adiabat

A line on a pressure versus volume diagram that describes its relationship for a specific case of adiabatic compression

adiabatic compression (equations)

(1) V*T^(f/2) = constant

(2) V^{gamma}*P = constant

V - volume

T - temperature

f - degrees of freedom

{gamma} - adiabatic exponent

= (f+2)/f

P - pressure

heat capacity (definition)

the amount of heat needed to raise an object's temperature, per degree temperature increase

heat capacity (equation)

C = Q/{Delta}T

Q - heat added

{Delta}T - change in temperature

specific heat capacity

c = C/m

C - heat capacity

m - mass of object

heat capacity at constant volume (definition)

The heat capacity of a body when its volume is kept constant and there is no work (W=0)

heat capacity at constant volume (equation)

C_V = ({delta}U/{delta}T)_V

V = constant, volume

U - total energy

T - temperature

heat capacity at constant pressure (definition)

The heat capacity of a body when its pressure is kept constant and work done and heat added are not zero

heat capacity at constant pressure (equation)

C_P = ({delta}U/{delta}T)_P+P*({delta}V/{delta}T)_P

or

C_P = ({delta}H/{delta}T})_P

P = constant, pressure

U - total energy

T - temperature

V - volume

H - enthalpy

heat capacity relation (equation)

C_P = C_V+N*k = C_V+nR

C_P - heat capacity at constant pressure

C_V - heat capacity at constant volume

N - number of molecules

n - number of moles

R - ideal gas constant

phase transition

alteration of the physical state of a substance, such as between a solid, liquid, or gas

latent heat (definition)

the amount of heat per unit mass required to melt or boil the substance completely

latent heat (equation)

L = Q/m

Q - heat required

m - mass of the substance

enthalpy (definition)

the total energy you would have to come up with, to create a system out of nothing and put it into the environment

enthalpy

H = U+P*V

U - total energy

P - pressure

V - volume

enthalpy of formation

the enthalpy change that accompanies the formation of a substance from the most stable forms of its component elements

equation of state

describes the macroscopic state of a system using the state variables

state variables

macroscopic, measurable quantities (P, V, T, etc.)

ideal gas vs Van der Waals equation

assumes that particles take up no volume, and do not have interaction potentials, while the other equation allows for these possibilities

work and heat

not state variables because they are not characteristics of a system and cannot be used to describe a system