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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

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)

Gas Law:

PV = RT

R is universal gas constant

R = 847.97 m kgf/kg mol ˚K

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

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%.

Thermal Expansion of Solids:

Thermal Conductivity:

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

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

T = absolute temperature, ˚K

K = proportionality constant

T1 = absolute temperature of cold body, ˚K

T2 = absolute temperature of hot body, ˚K

Newton’s Law of Cooling:

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

Kinetics Theory of Gas:

Specific Impulse:

Convective Heat Transfer: