Chapter 8: Second Law of Thermodynamics

Exa 8.1

In [1]:
#You are asked to comment on an inventor's claim that he has an engine which 
#delivers 25 Btu of work from an input if 100 Btu when it operates between 
#140F and 0F. Is the claim valid?
#initialisation of variables
W= 25 					#Btu
W1= 100 				#Btu
T1= 140 				#R
T2= 0 					#R
#CALCULATIONS
Th= T1+460. 			#T hot in Rankine
Tl= T2+460. 			#T cold in Rankine
nt= (Th-Tl)/Th 			#Max. efficieny
n= nt*100.
#RESULTS
print '%s %.2f' % ('maximum theotrical efficiency (percentage)((Claim is not valid)) = ',n)
raw_input('press enter key to exit')

maximum theotrical efficiency (percentage)((Claim is not valid)) =  23.33
press enter key to exit
Out[1]:
''

Exa 8.2

In [2]:
#Saturated steam in a rigid vessel is initially at 10 bar. heat is added
#until the steam s superheated at 38 bar and 310 C. What is the change in entropy?
#initialisation of variables
P= 10 						#bar
P1= 38 						#bar
T= 310 						#C
v= 64.03 					#cm^3/gm
s= 6.4415 					#J/gm K
vf= 1.12773 				#cm^3/gm
vg= 194.44 					#cm^3/gm
sf= 2.1387 					#J/gm K
sfg= 4.4478 				#J/gm K
#CALCULATIONS 
x= (v-vf)/(vg-vf) 			#x
sx= sf+x*sfg 				#Entropy
S= s-sx 					#Change in entropy
#RESULTS
print '%s %.3f' % ('Change in Entropy (J/gm K) = ',S)
raw_input('press enter key to exit')

Change in Entropy (J/gm K) =  2.856
press enter key to exit
Out[2]:
''

Exa 8.3

In [3]:
#If heat must be pumped at the rate of 70k Btu/hr to keep a house at 72F when
#the outside temperature is 15 F, What is the minimum power required to drive
#the heat pump?
#initialisation of variables
Qh= 70000. 							#Btu/hr
T= 15. 								#F
T1= 72. 							#F
#CALCULATIONS
COP= (T1+460)/((T1+460)-(T+460))	#Carnot efficiency
W= Qh/COP 							#Work
#RESULTS
print '%s %.2f' % ('Minimum power required to drive the heat pump (Btu/hr) = ',W)
raw_input('press enter key to exit')

Minimum power required to drive the heat pump (Btu/hr) =  7500.00
press enter key to exit
Out[3]:
''

Exa 8.4

In [4]:
#Heat must be pumped at the rate of 26kW to maintain a temperature of 43F
#in an air stream while the outside temperature is 0C. Determine 
#(a)the minimum electrical equipment in Kilowatts and 
#(b)the electrical requirement if an electric heater is used.
#initialisation of variables
h= 26. 								#KW
T= 43. 								#C
To= 0 								#C
#CALCULATIONS
COP= (T+273)/((T+273.)-(To+273.))	#Carnot efficiency
W= h/COP 							#Work
Qh=h 								#Heat
#RESULTS
print '%s %.2f' % ('Minimum electrical  requirement (KW) = ',W)
print '%s %.2f' % (' \n Elctrical requirement if an electrical heater used (KW) = ',Qh)
raw_input('press enter key to exit')

Minimum electrical  requirement (KW) =  3.54
 
 Elctrical requirement if an electrical heater used (KW) =  26.00
press enter key to exit
Out[4]:
''