Materials Thermodynamics Flashcards
State the 1st Law of Thermodynamics
dU = dQ - dW
If work is due to pressure forces dW = pdV
State the 2nd Law of Thermodynamics
s2-s1 = dQ/T + S_irreversible
What is the statistical interpretation of entropy
Entropy can be viewed as the no of microstates associated with a system.
dS = k_b ln(omega)
Recall the KE-Temperature Relationship
KE = 3/2 k_b T
How does stiffness vary depending on the material group?
Material stiffness is determined by the primary and secondary bonding.
- In Metals, ionic crystals and covalent solids stiffness is governed by the balance of electrostatic attraction and steric repulsion. This sets the atomic distance and rigidity.
- In foams cell-walls determine rigidity.
How does the polymer load response change when crossing the glass-transition temperature
- Below Tg, the thermal energy is insufficient to allow for the sliding of the polymer chains and so the stiffness is dependent on the rigidity of the chains.
- Above Tg, the polymers are viscoelastic (resist shear flow and strain linearly). The polymer chain is flexible and there is sufficient thermal energy for the polymer chains to flow. Over short time scales the chains become entangled and have an elastic response
What are Elastomers
Elastomers are formed of a cross-linked network of polymer chains. The cross-links are added to the polymer chain reducing monomer length. Thermosets are an example of elastomers
Outline the load response on Elastomers above and below the glass transition temperature
Elastomers do experience a drop in stiffness as they approach. Above Tg Elastomers remain solid and retain an elastic response. As the temperature rises further the stiffness of the elastomer network increases linearly l.
For T greater than Tg:
E = k_bT/ v_mn_c
v_m is the monomer volume
n_c is the no of monomers between cross-links
Qualitatively explain the micro-structural origin of the elastic response of polymers
First Law Thermodynamics dU = dQ - dW dW = -FdR So F = -T dS/dR This can be explained as stretching a polymer reduces the number of micro-states and thus the entropy of the system so dS/dR is negative.
Explain the origin of a restoring force when stretching a polymer chain.
As the temperature increases the Gibbs free energy function changes. This U and pV terms are unchanged however the TS term changes with the increasing temperature. Therefore there will be a large thermodynamic driving force to minimise G which results in a larger restoring force
What are the limitations of the Random Walk Model
- Assumes pin-joints between chains
- Does not take into account side-groups on the polymer chain
- Assumes chains are 2D so underestimates the number of configurations
What criteria define a phase
- Atomic Arrangement
2. Chemical Species Present
Derive an expression for the change in Gibbs free energy
G = U+pV-TS
dG = dU + pdV + Vdp - TdS - sdT
During Phase Transformations:
dp = dT = 0
Outline the relationship between the equilibrium state and Gibbs Free Energy
The equilibrium state corresponds to the minimum value of the Gibbs free energy. The thermodynamic driving force is set by the difference between the Gibbs energy at the current state and the minimum Gibbs energy. Note: a reaction is said spontaneous if dG is negative
Describe how the free energy change can be used to determine miscibility
If two materials are miscible then the entropy of mixing will be large and positive. This means the free energy will be lower than the unmixed case. The proportions of A and B corresponding to the lowest free energy is the equilibrium state.
