Internal Energy: is the sum of the kinetic energy of the molecules
due to its random motion & the potential energy of the molecules due to the intermolecular forces.
Internal energy is
determined by the values of the current state and is
independent of how the state is arrived at. Thus if a system undergoes a series of changes from one state A to another state B, its change in internal energy is the same, regardless of which path {the changes in the p & V} it has taken to get from A to B.
Since Kinetic Energy proportional to temp, and internal energy of the system = sum of its Kinetic Energy and Potential Energy, a rise in temperature will cause a rise in Kinetic Energy and thus an increase in internal energy.
If two bodies are in
thermal equilibrium, there is
no net flow of heat energy between them and they have the
same temperature. {NB: this
does not imply they must have the same internal energy as internal energy depends also on the
number of molecules in the 2 bodies, which is
unknown here}
Thermodynamic (Kelvin) scale of temperature: theoretical scale that is
independent of the properties of any particular substance.
An
absolute scale of temp is a temp scale which does not depend on the property
of any particular substance (ie the thermodynamic scale)
Absolute zero: Temperature at which
all substances have a
minimum internal energy {NOT: zero internal energy.}
T/K = T/°C + 273.15, by definition of the Celsius scale.
Specific heat capacity is defined as the amount of heat energy needed to produce
unit temperature change {NOT: by 1 K} for
unit mass {NOT: 1 kg} of a substance, without causing a change in state.
c = Q / mΔT
Specific latent heat of vaporisation is defined as the amount of heat energy needed to change
unit mass of a substance
from liquid phase to gaseous phase without a change of temperature.
Specific latent heat of fusion is defined as the amount of heat energy needed to change
unit mass of a substance
from solid phase to liquid phase without a change of temperature L = Q / m {for both cases of vaporisation & melting}
The specific latent heat of vaporisation is greater than the specific latent heat of fusion for a given substance because
 During vaporisation, there is a greater increase in volume than in fusion,
 Thus more work is done against atmospheric pressure during vaporisation,
 The increase in vol also means the INCREASE IN THE (MOLECULAR) POTENTIAL ENERGY, & hence, internal energy, during vaporisation more than that during melting,
 Hence by 1^{st} Law of Thermodynamics, heat supplied during vaporisation more than that during melting;
hence l_{v} > l_{f} {since Q = ml = ΔU  W}.
Note:
 the use of comparative terms: greater, more, and>
 the increase in internal energy is due to an increase in the PE, NOT KE of molecules
 the system here is NOT to be considered as an ideal gas system
Similarly, you need to explain why, when a liq is boiling, thermal energy is being supplied, and yet, the temp of the liq does not change.
 Melting  Boiling  Evaporation  Occurrence   Throughout the substance, at fixed temperature and pressure  On the surface, at all temperatures  Spacing(vol) & PE of molecules  Increase slightly  Increase significantly   Temperature & hence KE of molecules   Remains constant during process  Decrease for remaining liquid  First Law of Thermodynamics: The increase in internal energy of a system is equal to the sum of the heat supplied to the system and the work done on the system. [/t] ΔU: Increase in internal energy of the system Q: Heat supplied to the system W: work done on the system  {Need to recall the sign convention for all 3 terms} Work is done by a gas when it expands; work is done on a gas when it is compressed. W = area under pressure  volume graph. For constant pressure {isobaric process}, Work done = pressure x ΔVolume Isothermal process: a process where T = const {ΔU = 0 for ideal gas} ΔU for a cycle = 0 {since U ∝ T, & ΔT = 0 for a cycle } Equation of state for an ideal gas:
p V = n R T, where T is in Kelvin {NOT: °C}, n: no. of moles. p V = N k T, where N: no. of molecules, k:Boltzmann const Ideal Gas: a gas which obeys the ideal gas equation pV = nRT FOR ALL VALUES OF P, V & T Avogadro constant: defined as the number of atoms in 12g of carbon12. It is thus the number of particles (atoms or molecules) in one mole of substance. For an ideal gas, internal energy U = Sum of the KE of the molecules only {since PE = 0 for ideal gas}
U = N x^{½} m <c^{2}> = N x (3/2)kT {for monatomic gas}  U depends on T and number of molecules N
 U ∝ T for a given number of molecules
Ave KE of a molecule, ½ m <c^{2}> ∝ T { T in K: not °C } 

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