thermodynamics2 - temperature + entropy Flashcards
(32 cards)
what happens when a substance is heated + how does this help us determine energy used?
when a substance is heated, if there is a temperature ruse then C=q/ΔT
where C = specific heat capacity
rearrange to q = mCΔT
how does heat capacity change with different environmental factors?
heat capacity is different at constant pressure and constant volume
so Cp>Cv, and Cp - Cv = R (gas constant)
heat capacity can also vary with temperature
Cp = a + bT + c/(T^2), where a, b, anc c are empirical constants
why is heat capacity temperature dependent?
heat capacity is a dissipation term - measures the ability of a substance to absorb and dissipate within itself energy in form of heat
so at very low temps, only transitions possible will be between energy levels which are very close together (translational) where not much energy is needed to travel between levels
vs at high temps where many more transitions are possible and transitions are more costly, which causes heat capacity to increase
how are degrees of freedom distributed among atoms?
every atom has 3 degrees of freedom (up/down, forward/back, left/right) - these are the only possible movements of atoms
degrees of freedom must be conserved
outline the occupation of energy levels at different temperatures for diatomic H2 molecule
at low temps, only translational levels are occupied
at room temp, rotational energy levels are occupied and heat capacity increases
at high temps the dissociation temp for vibrational energy levels has been reached and these levels are now also occupied
how does degrees of freedom impact heat capacity for ideal gases?
greater degrees of freedom means higher heat capacity
every electronic, rotational and vibrational degree of freedom contributes (1/2)R to heat capacity - only degrees of freedom which are active/occupied can contribute to the heat capacity of a material
- internal energy works similarly, except translational rotational and vibrational degrees of freedome have a contribution of (1/2)RT
why is reaction enthalpy temperature dependent?
heat capacity of products and reactants are different at different temperatures - consider how much temperature rises for a given amount of energy depends on heat capacity
what is kirchoffs law + its purpose?
kirchoffs law approximates the change to enthalpy of reaction for moderate temperature changes
ΔrH° (T’) = ΔrH°(T) ~+ ΔrCp°(T’ - T)
where ΔrCp° = Cp products - Cp reactants
latent heat definition
energy required to change state/phase (not increasing temp)
what changes will and won’t be seen during a phase transition?
phase transitions are accompanied by a change in enthalpy of the system but no change in temperature
is enthalpy of vapourisation < or > than enthalpy of fusion + why
enthalpy of vapourisation is always > enthalpy of fusion, this is because when moving to a gas phase intermolecular bonds need to be completely broken, this requires a large amount of energy
how can you achieve perfect engine efficiency?
engine efficiency depends on the temp difference between source and sink, a greater difference = more efficient
so for a perfectly efficient engine/system, you need Tsink = 0 or Tsource = infinity
- this is how kelvin came up with the value for absolute 0
what is the second law of thermodynamics - give the 4 versions/interpretations
‘no repeatable/cyclic process is possible in which heat is taken from a hot source and completely converted into work’ - kelvins version
‘heat does not pass from a body at low temperature to one at high temperature without an accompanying change elsewhere’, such as work - this is clausius’ version, about fundamental flow of heat
‘the entropy of an isolated system tends to increase’
‘the entropy of a universe increases during any spontaneous change’
what is entropy change in a system according to clausius?
clausius defined the change in entropy of a system as = to heat supplied/temp
how does temperature affect entropy change?
the change in entropy at low temperatures is considerably higher than at high temps, for the same input of heat energy - this is why absolute 0 is so hard to reach, even if the tiniest amount of heat enters the system the changes are massive
why does gas distribute evenly on a molecular level, statistically?
the system will take up the macrostate which is most probable, which is always the more evenly distributed/the one with the most microstates - it is very improbable in the real world for gas molecules to cluster themselves, therefore it will not happen, ever, although not technically impossible - this kind of idea is the basis of the infinite improbability drive
multiplicity, Ω definition + equation
the number of microstates making up a single number of microstates
Ω = N!/na!nb!
where N! = total number of atoms factorial
a = state we want
b = all other states
probability of being in any particular macrostate is Ωa = Ω/N!
how can entropy be defined by multiplicity?
S = Kb lnΩ
this is from a theoretical statistical approach derived by boltzmann
how does multiplicity relate to entropy?
we know the most probably macrostate is the one with the most microstates
statistical definition of entropy also suggests that the most probable outcome is the one with the highest entropy, therefore if the universe tends towards high probability, it tends towards disorder
how does temperature affect entropy?
as temp increases, the particles occupy more energy levels and there are more possible microstates so the probability of being in any particular level has decreased but overall entropy of system increases
as temp tends towards 0, entropy change of system is massive
absolute 0 definition
when all atoms are in ground state energy level
how are heat capacity and entropy related?
when heat capacity isn’t the same across the range of temps, the area under a plot of Cp against T will give ΔS
the absolute entropy at a given temp is the area under the graph of Cp/T between absolute 0 and the temperature of interest
- however entropy of fusion/vapourisation/etc must be considered - at phase changes there will be a sharp increase in entropy with no temperature change
how are entropy and temperature related?
the increase in entropy with increasing temperature follows the same logarithmic relationship regardless of if its heated at a constant volume or pressure
why can ΔS be given in the form ΔS = ΣS(products) - ΣS(reactants) ?
because it is a state function
