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 Engineering Formulae
  Thermodynamics and Heat Transfer
 

 

 

 

 

Boyle’s Law:

If the temperature (T) remain constant, the volume (V) of a given mass of gas is inversely proportional to the pressure (P)

or         PV= constant at a given temperature

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Charle’s Law

(a)   If the pressure (P) is held constant, the volume (V) of a given mass of gas varies directly as the absolute temperature (T)

                

(a)   If the volume (V) is held constant, the pressure (P) of a given mass of gas varies directly as the absolute temperature (T)

                         

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Gas Law:

PV = RT

            R is universal gas constant

            R = 847.97 m kgf/kg mol ˚K

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Enthalpy of an Ideal Gas:

The property of enthalpy, H is defined as:

where

            U=internal energy of an ideal gas

            P=pressure

            V=total volume

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Specific Volume: 

or                    

where,

            v=specific volume, m3/kg

            x=quality of the mixture

             1-x=moisture fraction of the mixture

            =specific Volume of dry and saturated steam at a particular pressure, m3/kg

            =specific volume of saturated water, m3/kg

             = change in specific volume during evaporation

                  =

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Entropy of Steam

Change in entropy during heating of water and its evaporation into steam is given by

where,

            =change in entropy

                C=specific heat

                   =I for steam

               T1=initial temperature

               T2=final temperature

               Ts=steam temperature

                X=dryness fraction at final state of steam

                L=latent heat

Latent heat of fusion=80 kcal/kg

Latent heat of evaporation=539.6 kcal/kg

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Flow Energy:

Flow energy=work done by a system

                   = pv

where,

            p=pressure

            v=AΔd for unit mass

            A=area of piston

            Δd=displacement

Internal energy =u (for unit mass flow)

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Law of Thermodynamics

First Law: When a system undergoes a thermodynamics cycle then the net heat (Q) supplied to the system from its surrounding is equal to the net work(W) done by the system on its surrounding.

            In symbols,

Second Law: It is impossible for a heat engine to produce net work (W) in a complete cycle if it exchanges heat only with bodies at a single fixed temperature.

             Net heat supplied = Net work done

           

Thermal efficiency

 

It can be seen that the second law implies that the thermal efficiency of a heat engine must always be less than 100%.

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Thermal Expansion of Solids:

 

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Thermal Conductivity:

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Latent Heat of Fusion and Vaporization:

where,             H = quantity of heat required or liberated, cal

                        m = mass of a given substance to be fused or solidified, g

                        Lf = latent heat of fusion, cal/g

                   Lv = latent heat of vaporization, cal/g

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Black Body Radiation:

where,              E = energy radiated per second by a body, cal/cm2.s

                        T = absolute temperature, ˚K

                        K = proportionality constant

                        = difference in energy radiation

                        T1 = absolute temperature of cold body, ˚K

                        T2 = absolute temperature of hot body, ˚K

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Newton’s Law of Cooling:

By expanding the quantity in parenthesis and neglecting for small temperature difference, we find

 

Kinetics Theory of Gas:

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Specific Impulse:

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Solar Radiation:

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Convective Heat Transfer:

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Radiation Heat Transfer:

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Conduction Heat Transfer:

 

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