Requirement of temperature scale - thermodynamics, Mechanical Engineering

Requirement of Temperature Scale:

The temperature scale on which temperature of the system can be read is required to assign the numerical values to the thermal state of the system. It requires the selection of basic unit and reference state.

Establish a correlation between Centigrade and Fahrenheit temperature scales.
Sol:
Let the temperature't' be linear function of property x. (x can be length, resistance volume, pressure etc.) Then by using equation of Line;

t = A.x + B                                                                                                                         ...(i)

At Ice Point for Centigrade scale t = 0°, then

0 = A.xi  +B                                                                                                                         ...(ii)

At steam point for centigrade scale t = 100°, then

100 =A.x S + B                                                                                                                      ...(iii)

From equation (iii) and (ii), we get

a = 100/(xs - xi ) and b = -100xi/(xs  - xi) Finally equation becomes in centigrade scale is;

t0 C = 100x/(xs  - xi ) -100xi/(xs  - xi)

t0 C = [(x - xi )/ (xs  - xi )]100                                                                                           ...(iv)

Likewise if Fahrenheit scale is used, then

At Ice Point for Fahrenheit scale t = 32°, then

32 = A.xi  + B                                                                                                                        ...(v)

At steam point for Fahrenheit scale t = 212°, then

212 =A.xS + B                                                                                                                       ...(vi)

From equation (v) and (vi), we get

a = 180/(xs  - xi ) and b = 32 - 180xi/(xs  - xi) Finally general equation becomes in Fahrenheit scale is;

t0 F = 180x/(xs  - xi ) + 32 - 180xi/(xs  - xi)

t0 F = [(x - xi )/ (xs  - xi )]180 + 32                                                                                ...(vii)

Likewise if Rankine scale is used, then

At Ice Point for Rankine scale t = 491.67°, then

491.67 = A.xi  + B                                                                                                                    ...(viii)

At steam point Rankine scale t = 671.67°, then

671.67 = A.xS + B                                                                                                                      ...(ix)

From equation (viii) and (ix), we get

a = 180/(xs  - xi ) and b = 491.67 - 180xi/(xs  - xi) Finally equation becomes in Rankine scale is;

t0 R = 180×/(xs  - xi ) + 491.67 - 180xi/(xs  - xi)

t0 R = [(x - xi )/ (xs  - xi )] 180 + 491.67                                                                        ...(x)

Likewise if Kelvin scale is used, then

At Ice Point for Kelvin scale t = 273.15°, then

273.15 = A.xi  + B                                                                                                                      ...(xi)

At steam point Kelvin scale t = 373.15°, then

373.15 = A.xS + B                                                                                                                     ...(xii)

From equation (xi) and (xii), we get

a = 100/(xs  - xi ) and b = 273.15 - 100xi/(xs  - xi) Finally equation becomes in Kelvin scale is;

t0 K = 100x/(xs  - xi ) + 273.15 - 100xi/(xs  - xi)

t0 K = [(x - xi )/ (xs  - xi )] 100 + 273.15                                                                    ...(xiii)

Now compare between above four scales:

(x - xi )/ (xs  - xi ) = C/100                                                                                           ...(A)

= (F-32)/180                                                                                                                ...(B)

= (R-491.67)/180                                                                                                         ...(C)

= (K - 273.15)/100                                                                                                     ...(D)

Now joining all 4 values we get following relation

K = C + 273.15

C = 5/9[F - 32]

= 5/9[R - 491.67] F = R - 459.67

= 1.8C + 32

 

Posted Date: 10/15/2012 2:08:25 AM | Location : United States







Related Discussions:- Requirement of temperature scale - thermodynamics, Assignment Help, Ask Question on Requirement of temperature scale - thermodynamics, Get Answer, Expert's Help, Requirement of temperature scale - thermodynamics Discussions

Write discussion on Requirement of temperature scale - thermodynamics
Your posts are moderated
Related Questions
Classification Based on Mode of Welding Manual welding: In this welding the entire welding operation is performed and controlled by hand. Here, there are two movements involv

Find out the components of the force: The frame of a certain machine accelerates to the right at 0.8 g m/sec 2 . As illustrated in Figure, it carries a uniform bent bar ABC we

A combined cycle plant is designed to develop 200MW power. The air is obtained by the compressor at 300K and 1 bar pressure. The maximum temperature of the gas turbine cycle is lim

Find out stress - strain and elongation of bar: A circular rod having diameter 20 m and 500 m long is subjected to the tensile force of 45kN. The modulus of elasticity for st

Design the bending moment and shear force diagram for a simply supported beam of length 9 m and carrying a Uniformly distributed load of 10 KN /m for a distance of 6 m from the lef

Explain the working of Michelson's interferometer. How circular fringes he produced with it. (a) What are antireflection films and interference filters? (b) Find the reflecti

#constructional features and working of Multiplate Dry Clutch

Once vendor drawings are received and piping isometric drawings are prepared, the Mechanical engineer will provide a final stress package to the stress engineer per The stress a

the base of a spring -mass- damper system is subjected to the periodic displacement. determine the response of the mass using the principle of superposition

Q. Can you explain the Mobile bed model? Mobile bed models can again be either geometrically similar or vertically exaggerated. Models of the former type permit study of proble