09 Thermal Properties Flashcards
- Define heat capacity and specific heat.
heat capacity represents the quantity of heat required to produce a unit rise in temperature for 1 mole of a substance [J/molK]
on a per-unit-mass basis i.e. required heat for a unit rise in temperature per kg [J/kgK], it is termed specific heat (capacity) cp
heat capacity is normally an extensive property but when divided by the mol or kg (prefix: molar and specific, respectively) of the system it gets an intensive property.
- Note the primary means by which thermal energy is assimilated by solid materials.
most of the energy assimilated (anpassen) by solid materials is associated with increasing the vibrational energy of the atoms
- Define phonon.
Regarding the vibrational energy of atoms upon heating only specific vibrational energy values are allowed (then energy is said to be quantized); a single quantum of vibrational energy is called a phonon
- Cite the equation for the low-temperature temperature dependence of heat capacity at constant volume.
at low temperatures:
Cv = A*T^3
Cv…heat capacity at constant volume
A…temperature independent constant
T…temperature
- Define Debye temperature.
Above the Debye temperature θD , Cv levels off and becomes essentially independent of temperature at a value of approx. 3R, R being the gas constant.
- At temperatures in excess of the Debye temperature, cite the approximate value for the constant volume heat capacity.
Cv = 3R (approximately)
R = 8.314 J/molK (gas constant)
Hence for solid metallic materials at room temperature Cv = 25 J/molK (approx.), because the Debye temperature is less than TR for many solid materials.
However, for the value Cv for a ceramic material is approx. 25 joules per mole of ions. Therefore Cv for e.g. Al2O3 is 5*25=125 J/molK, given the fact there are five ions per formula (Al2O3) unit.
- Determine the linear coefficient of thermal expansion given the length alteration that accompanies a specified temperature change.
- For an isotropic material, estimate the volume coefficient of thermal expansion from the linear value.
ΔV/V0 = αV * ΔT
αV …volume coefficient of thermal expansion
Although in many materials the value αV is anisotropic.
- Briefly explain the phenomenon of thermal expansion from an atomic perspective using a potential energy-versus-interatomic separation plot.
In the Lennard-Jones potential, by heating the interatomic separation increases from r0 to r1 to r2, and so on.
in a symmetric energy potential, there is no increase in interatomic separation
- Make a qualitative comparison of the coefficients of thermal expansion for metals, ceramics, and polymers.
Polymers have larger α values because of the weak secondary bonds (van-der-Waals bonds)
With increasing bond energies the α-values are decreasing.
- Define thermal conductivity.
The transport of thermal energy from high- to low-temperature regions of a material is termed thermal conduction.
- (a) Note the two mechanisms of heat conduction.
(b) Compare the relative magnitudes of these contributions for each of metals, ceramics, and polymeric materials.
a) conduction heat is transported by free electrons and by vibrational lattice waves, or phonons.
b) high thermal conductivities for rel. pure metals are due to the large numbers of free electrons and the efficiency with which these electrons transport thermal energy, e- are not easily scattered like phonons and have higher velocities, the phonon contribution is much less efficient
ceramics and polymers are poor thermal conductors because free e- concentrations are low and phonon conduction predominates
- For an isotropic solid material which ends are restrained by rigid supports, calculate the thermal stress that results from a specified temperature change, given values of the elastic modulus and coefficient of thermal expansion.
thermal stress occurs due to:
- restrained thermal expansion/contraction
- temperature gradients that lead to differential dimensional changes
- Explain the establishment of thermal stresses as a body of material is heated or cooled.
sources:
- restrained thermal expansion (or contraction) of a body
- can also result from the rapid heating or cooling of a body of material whereby temperature gradients between the outside and interior portions and accompanying differential dimensional changes occur
- Estimate the thermal shock parameter for a material given its fracture strength, thermal conductivity, modulus of elasticity, and linear coefficient of thermal expansion.
thermal shock is the fracture of a body resulting from thermal stresses induced by rapid temperature changes. Because ceramic materials are brittle, they are especially susceptible to this type of failure.
(quench rate)for fracture = TSR ≈ σf*k/(E*αl)
σf …fracture strength
k…??
E…elastic modulus
max. temperature change ΔTf w/o thermal shock (=fracture):
ΔTf = σf/(E*αl)
Why is cp larger for polymers compared to metals and ceramics?
The linear coefficient of thermal expansion of polymers is much higher than metals. Whatever amount of heat they absorb from surrounding or any other source, most of them is used in increasing interatomic distance rather than increasing the temperature of the polymer. The highest values in polymers are found among linear and branched polymers as they can expand more because of the lack of a large number of intercrossing.
Furthermore, polymers are covalently bonded material and metals are metallicly bonded material. Covalent bonds do not let atoms exchange electrons like metallic bonds do.
Fourier´s Law?
