Thermodynamics Second Law Flashcards
How would you define a heat engine?
A system which diverts some heat energy (which flows from hot to cold) to do work
What property must the most efficient possible heat engine have?
It must be reversible, otherwise friction diverts heat energy into the surroundings without doing work
What is a Carnot Engine?
A carnot engine is a hypothetical heat engine that:
- Has two thermal reservoirs (hot and cold)
- Operates in a cycle using a working substance
- Is reversible
Describe a diagram showing the operation of a Carnot Engine
Qh is the heat extracted from the reservoir per cycle
Qc is the heat delivered to the cold reservoir per cycle
W is the work done per cycle
The engine can also be run in reverse, to drive heat from cold to hot.
Describe the p-V diagram respresenting a Carnot Cycle
Curves TU and TL are isotherms, where TU is the temperature of the heat reservoir and TL is the temperature of the cold reservoir. These curves show heat and work being exchanged.
Curves BC and DA are adiabatic curves, which show internal energy and work being exchanged. There is no change in heat energy for these curves.
When work is done by the system on the surroundings, that work is negative, and vice versa.
Define the efficiency of a Carnot Engine
Define Clausius’ statement
It is impossible to transfer heat spontaneously from cold to hot without causing other changes
Define Thomson’s statement
A process whose only effect is the complete conversion of heat to work is impossible
Explain how the Clausius statement disallows the existence of a heat engine more efficient than a Carnot engine
Suppose we have two identical Carnot engines, each driving the other in reverse. If the driving engine were more efficient than a Carnot engine, it would extract less heat to perform the same amount of work. The net effect would be Qh-Qh’’ > 0, which violates the Clausius statement
Define Carnot’s Theorem
No engine operating between two thermal reservoirs can be more efficient than a Carnot Engine operating between the same two reservoirs
Define the fundamental limit of efficiency of a heat engine
Provided we define temperature such that Tc=Qc and Th=Qh
In a Carnot cycle, what is the implication of replacing the isothermal expansion step (which is reversible) with an adiabatic free expansion step (which is irreversible)?
Since any cycle can be represented as a sum of Carnot cycles, we can make this sum an integral for any reversible cycle doing work.
Define the state function Entropy
S it the entropy of a system; dS=dQrev/T, where dS is an exact differential
Describe the Law of Increase of Entropy for:
- An infinitesimal process
- An isolated system
- The universe
For an infinitesimal process, dS ≥ ¯dQ/T (the equality shows the process is reversible)
For an isolated system, since ¯dQ=0, dS ≥ 0
For the whole universe, dS ≥ 0 for any real process
What is the final equilibrium state of any isolated system?
A state which maximises the entropy of the system
What is the change in entropy for isothermal expansion?
What is the change in entropy for adiabatic free expansion?
Q = 0 so ∆S ≥ ∫¯dQ/T so ∆S ≥ 0
We cannot calculate this directly, but since S is a state function, ∆S must be the same as for isothermal expansion (nR ln Vf/Vi).
How can we calculate the entropy change for real, irreversible processes e.g. adiabatic free expansion?
Via equivalent, reversible processes e.g. isothermal expansion
How would you derive the statistical interpretation of entropy?
Consider the adiabatic free expansion of 1 mole of an ideal gas such that it doubles its volume: ∆S = R ln Vf/Vi = R ln 2.
How many ways can N atoms be arranged between m cells? Ω = m^N. So the number of arrangements for 2m cells is Ω = (m^N)^2 = m^2N.
If we define S = k ln Ω, ∆S = k * N ln 2m - k * N ln m = N k ln 2, so ∆S = R ln 2 as above
How does entropy depend on temperature at fixed pressure?
In a single phase, dS = ¯dQrev/T = Cp dT/T
At phase transition, ∆S = Qrev/T = L/T (L = latent heat)
We can therefore calcualate S(T) from measurements of Cp(T)
What is the third law of thermodynamics?
S (T=0) = 0
S(T) can therefore be put on an absolute scale
Using two different expressions of the first law of thermodynamics, define pressure and temperature
T= ∂U/∂S with constant volume; p = -∂U/∂V with constant entropy.
Using the First Law of Thermodynamics and the equations of state pV=nRT and U=3/2 nRT, derive the entropy and energy fundamental equations for an ideal monoatomic gas.
Where U0, V0 and S0 define a reference state.
We can take partial derivatives w.r.t. entropy and volume to derive U=3/2 nRT and pV=nRT from this equation.
Define and describe the Hemholtz free energy of a system
F=U-TS
The Hemholtz free energy is a measure of the amount of energy needed to create a system, once the spontaneous energy transfer to the system from the environment is accounted for.
Define and describe the enthalpy of a system
H = U + PV
The enthalpy of a system is the internal energy of a system plus the “PV” work done by that system.
Define and describe the Gibbs free energy of a system
G = U - TS + PV = H - TS
The net energy contribution for a system at temperature T after PV work is done to expand the system from a negligible initial volume.
Describe the thermodynamic Legendere Transforms
F = U - TS, G = H - TS, H = U + pV
Transforms dU = T dS - p dV into the other ‘natural variables’, preferably (V, T) or (p,T)
