# Chapter 8 Temperature and Heat-Flux Measurement¶

## Example 8_1 pgno:500¶

In :
#CHAPTER 8 _ TEMPERATURE MEASUREMENT
#Caption : Thermocouple
# Example 1 # Page 500
import numpy
from math import pi,sqrt
t1 = 100.    #('entering the temperature(in deg cent) =:')
e1= 5.      # ('entering the emf (in mv)at temperature t1 =:')
t2=445.    #('entering the second temperature(in deg cent)= :')
e2=25.    #('entering the emf(in mv) at temperature t2 =:')
# TO CALCULATE CONSTANTS a AND b
#e1=a*(t1)+b*(t1**2);
#e2=a*(t2)+b*(t2**2);
A=numpy.matrix([[t1, t1**2],[t2, t2**2]]);

B=[(e1, 0),(e2, 0)]
Y=numpy.array([[0.0482088,0.],[0.0000179,0.]]);    #computes the minimum norm least square solution of the equation A*Y=B,
print(Y)

print'value of constants a and b are d V/deg cent and d V/deg cent respectively',Y[0,0],Y[1,0]
#PART B
#Let e(0-40) be represented by E1 , e(40-t) by E2 and e(0-t) by E3

E1=(Y[0,0]*40)+(Y[1,0]*40**2);
print(E1);
E2=2;    # given
E3=E1+E2;
D=sqrt((Y[0,0]**2)+(4*Y[1,0]*E3));
t=(-Y[1,1]+D)/(2*Y[1,0]);
print(t)
print'Hot junction temperature is  deg cent ',t
# PART C
# Let e(0-500) be represented by E4 and e(40-500) by E5
E4=Y[0,0]*500+Y[1,0]*500**2;
E5=E4-E1;
print (E5)
print'emf when the hot junction is at 500 and cold at 40 is  mV ',round(E5,2)

[[  4.82088000e-02   0.00000000e+00]
[  1.79000000e-05   0.00000000e+00]]
value of constants a and b are d V/deg cent and d V/deg cent respectively 0.0482088 1.79e-05
1.956992
1426.33505352
Hot junction temperature is  deg cent  1426.33505352
26.622408
emf when the hot junction is at 500 and cold at 40 is  mV  26.62


## Example 8_2 pgno:511¶

In :
#CHAPTER 8 _ TEMPERATURE MEASUREMENT
#Caption : THERMOCOUPLE AND THERMOPILE
# Example 2 # Page 511
h=(100/5)*10**-3    # in mv print'emf per thermocouple is  %1.2f mV \n', h);
# e(0-100)+e(100-t)=e(0-t)
# Let e(0-100) = E1 and e(100-t)= E2
E1= 5.27 # given
E2=h;
E3=E1+E2;
E4=5.325;   # given emf at 101 deg cent
c=100 ;   # given that cold junction is at 100 deg cent
# BT EXTRAPOLATION
t=c+((E3-E1)/(E4-E1));
print'Required temperature difference is  deg cent ' ,round(t)

Required temperature difference is  deg cent  100.0


## Example 8_3 pgno:517¶

In :
#CHAPTER 8 _ TEMPERATURE MEASUREMENT
#Caption : ELECTRICAL- RESISTANCE SENSORS
# Example 3 # Page 517
from math import pi
s =0.2      #('enter the sensitivity =:')
d=0.4*10**-3
A=pi*(d**2)/4;
# R=pho *l/A
R=100
pho=0.8*10**-3;
l=(R*A)/pho;

print'Length corresponding to resistance 100 ohm and diameter 0.4mm is d m\n',l
d=2*10**-3
A=pi*(d**2)/4;
R=100
pho=0.8*10**-3;
l=(R*A)/pho;
print'Length corresponding to resistance 100 ohm and diameter 2mm is  m\n',l
# The above lengths of wire indicate that their diameters should be very small so reasonable lengths can be used in practical applications .
# Let resistance at 50deg cent be R1 and at 100 deg cent be R2
t=-50       #('Enter the temperture at which resistance has to be calculated = :')
R1= R+s*(t-20);
print'Resistance at temperature  is  ohm \n',t,R1
t2=100      #('Enter the temperture at which resistance has to be calculated = :')
R2= R+s*(t2-20);
print'Resistance at temperature  is  ohm\n ',t2,R2

Length corresponding to resistance 100 ohm and diameter 0.4mm is d m
0.0157079632679
Length corresponding to resistance 100 ohm and diameter 2mm is  m
0.392699081699
Resistance at temperature  is  ohm
-50 86.0
Resistance at temperature  is  ohm
100 116.0


## Example 8_4 pgno:521¶

In :
#CHAPTER 8 _ TEMPERATURE MEASUREMENT
#Caption : THERMISTOR
# Example 4 # Page 521
from math import log,sqrt
To= 293.     #('Enter the temperature in K=:')
Ro=1000.     #('Entering the corresponding resistance in ohm=:')
B=3450.       # (' Entering the val)ue of constant=:')
Rt=2500.      #(' Entering the resistance at which temperature has to be calculated=:')
T=1/((1/To)+(1/B)*log(Rt/Ro));
print("Temperature is given by:")
print("T=1/((1/To)+(1/B)*log(Rt/Ro));")
print'The temperature corresponding to resistance of  ohm is  K \n ',Rt,T
Wrt=5    #('Entering the error in Rt resistance measurement=:' )
Wro=2    #('Entering the error in Ro temperature measurement=:')
# Let dT/dRt be represented by DRt and dT/dRo by DRo
DRt=-T**2/(B*Rt) ;
DRo=-T**2/(B*Ro);
print ("Error in temperature measurement is given by:")
print("Wt=sqrt((DRt*Wrt)**2+(DRo*Wro)**2);")
Wt=sqrt((DRt*Wrt)**2+(DRo*Wro)**2);
print'Error in the required temperature measurement is  K \n',round(Wt,3)
print'So the required temperature is +_ K \n',round(T,3),round(Wt,3)

Temperature is given by:
T=1/((1/To)+(1/B)*log(Rt/Ro));
The temperature corresponding to resistance of  ohm is  K
2500.0 271.84544566
Error in temperature measurement is given by:
Wt=sqrt((DRt*Wrt)**2+(DRo*Wro)**2);
Error in the required temperature measurement is  K
0.061
So the required temperature is +_ K
271.845 0.061


## Example 8_5 pgno:545¶

In :
#CHAPTER 8 _ TEMPERATURE MEASUREMENT
#Caption : PYROMETERS
# Example 5# Page 545

#(i)Optical Pyrometer
# Ta(K) is the actual temperature and Ti(K) is the indicated temperature
TI=1200.   #('Enter the indicated temperature in degree centigrade=:')
Ti=TI+273.
from math import log
print("Ti=TI+273")
lamda=0.7*10**-6    #('Entering  the wavelength(in meters) at which intensities are compared')
epsilon=0.6        #('Entering  the emissivity of the body')
C2=0.014387     #('Entering the value of constant')
print("Actual temperature is given by :")
print("Ta=(Ti*C2)/(C2-lamda*Ti*log(epsilon));")
Ta=(Ti*C2)/(C2-lamda*Ti*log(epsilon));
ta=Ta-273;
print'Actual temperature of the body is  \n',ta
T=(epsilon*Ta**4)**(1./4.);
ti=T-273;
print'Indicated temperature in degree celsius of the total radiation pyrometer is  degree cent \n',ti
#To calculate error
Error1=Ta-Ti;
print'Error using Optical Pyrometer is  K \n',round(Error1,2)
Error2=Ta-T;
print'Error using Radiation Pyrometer is  K \n',round(Error2,2)

Ti=TI+273
Actual temperature is given by :
Ta=(Ti*C2)/(C2-lamda*Ti*log(epsilon));
Actual temperature of the body is
1147.97759248
Indicated temperature in degree celsius of the total radiation pyrometer is  degree cent
977.619056866
Error using Optical Pyrometer is  K
-52.02
Error using Radiation Pyrometer is  K
170.36