# Thermal Physics

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 1st Law of Thermodynamics, heat supplied during vaporisation more than that during melting;
hence lv > lf {since Q = ml = ΔU - W}.

Note:

1. the use of comparative terms: greater, more, and>
2. the increase in internal energy is due to an increase in the PE, NOT KE of molecules
3. 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.

 ΔU = W + Q 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 carbon-12. 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 x½ m <c2> = 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 <c2> ∝ T { T in K: not °C }