Microscopic Energy

P M V SubbaraoProfessor

Mechanical Engineering Department

A Thermodynamic Property of Substances…..

Hydro Electric Plant : The Work Done by A Falling Water Ligament patm

H

psur = patm

Microscopic Energy

• This energy is defined as the energy associated with the random, disordered motion of molecules and due to intermolecular forces.

• It is separated in scale from the macroscopic ordered energy associated with moving or stationary objects;

• It refers to the invisible form of energy at atomic and molecular scales.

• Popularly known as Internal Energy, U.

Internal (Microscopic) Energy : Ideal Gas

• Internal energy involves energy at the microscopic scale.

• Potential and Kinetic energies of individual molecules/atoms.

• But the potential energy is associated with intermolecular forces which are presumed to be zero in an ideal gas.

• Therefore the internal energy of an ideal gas is entirely kinetic energy.

Internal (Microscopic) Energy : Monatomic Ideal Gas

• For an ideal monatomic gas, this is just the translational kinetic energy of the linear motion of the "hard sphere" type atoms.

TRnU ~

2

3~

TmRU 2

3

For a monatomic ideal gas this change in internal energy is given by :

Internal (Microscopic) Energy : Diatomic Ideal Gas

• For polyatomic gases there is rotational and vibrational kinetic energy as well.

Internal (Microscopic) Energy : Polyatomic Ideal Gas

Internal (Microscopic) Energy : Other Substances

• Then in real gases, liquids and solids there is potential energy associated with the intermolecular attractive forces.

Increase of Internal Energy

Supply enough heat to each of these systems till the there is 1C increase in temperature.

Internal Energy and Temperature

Internal Energy of an Ideal Gas

• Internal energy in general includes both kinetic energy and potential energy associated with the molecular motion.

• But the potential energy is associated with intermolecular forces which are presumed to be zero in an ideal gas.

• Therefore the internal energy of an ideal gas is entirely kinetic energy.

• For a monoatomic ideal gas this change in internal energy is given by

•If rotation and vibrational kinetic energies are involved (polyatomic molecules) then

TnRU 2

3

TnRf

U 2

f : Number of degrees of freedom of a molecule

Means to Measure Energy

• Macroscopic Energy: Easy to measure.

• Microscopic Energy: Needs a detailed experiment.

• Identify methods to measure economically.

Measurement of Change in Internal Energy

• First law for A control mass:

Constant Volume Heating 1Q2 = U2 – U1

pdVdUQ

• Consider a homogeneous phase of a substance with constant composition.

• Define Specific Heat: The amount of heat required per unit mass/mole to raise the temperature by one degree.

• No change in other forms of energy, except internal energy.

Constant Volume Specific Heat

• The molar specific heat at constant volume is defined by

• For a monatomic ideal gas,

1212 2

3TTnRUU

TnRf

U 2

CV Specific Heats of Ideal Gases

Experimental results

GasConstant Volume Heat Capacity

CV(J/mol K) CV/RAr 12.5 1.50He 12.5 1.50CO 20.7 2.49H2 20.4 2.45HCl 21.4 2.57N2 20.6 2.49NO 20.9 2.51O2 21.1 2.54Cl2 24.8 2.98CO2 28.2 3.40CS2 40.9 4.92H2S 25.4 3.06N2O 28.5 3.42SO2 31.3 3.76

Polytropic Process of A Control Mass

• Polytropic process of a control mass:

n

R

TT

uuCn

112

12

pdvduq

Measurement of Changes during Constant Pressure Process

• Constant pressure heating of a control mass:

Constant Pressure Heating 2121 WUQ

1221 VVpUQ

Changes during Constant Pressure Process

• Infinitesimal constant pressure heating process by a control mass:

Constant Pressure Heating

WdUQ pdVdUQ VdpVdppdVdUQ

pVddUQ The quantity pV is also having a behaviour of property !This is called flow energy, flow work or internal work.However, the significance of this property is not felt in a Control Mass.

pVUdQ

Another way of representing this effect is to combine U and PV.Let this be H.

The issue of Increasing unit Temperature of A Pure Substance

Flow Work or Flow Energy• Unlike control mass, control volumes involve mass flow across

their boundaries.

• The substance inside a control volume will be at some pressure, temperature…..

• The fluid entering the control volume is pushing itself against the pressure of the control volume.

• Some work transfer is involved in pushing this mass into the control volume.

• This is an internal work.

• This is called flow work or flow energy.

Visualization of Flow Work

• F= pA will be a driving force responsible for the pushing of the fluid into the CV.

• This force will perform a work transfer of F.L to push the fluid.

• Therefore, the flow work = F ×L = p × A × L = p × V• This can exists even when there is a fluid pushed out of the

CV.

pF

L

Flow work

• It is interesting to note that unlike other work quantities, the flow work is expressed in terms of state variables.

• This is also a state variable, point function and hence a thermodynamic property.

• This is also called flow energy, convected energy or transport energy.

• The total energy of non flowing fluid: E = m(u + ½V2 + gz)

• The total energy of flowing fluid: =m(u + pv + ½V2 + gz).

• This total energy is also called as Methalpy.

• The term u + pv is called as specific Enthalpy, h.

Energy transport by Moving fluid

• Amount of energy transport by a moving fluid of mass m:

= mθ = m ( h + ½V2 + gz )

• Rate of Energy Transport:

gz

Vhm

2

2

Internal Energy & Enthalpy of Wet Mixtures

• x is the dryness fraction.

• U = (1-x) Uf + x Ug

• Specific Internal energy: Internal energy per unit mass ; u

• u = (1-x) uf + x ug

• Specific enthalpy

• h = (1-x) hf+ x hg

T

u uguf

ufg