Chapter 3 : Work and Heat Transfer

Example 3.1 Page No : 57

In [1]:
import math 

# Variables
V1 = 100.; 			# Initial velocity in m/s
g = 9.81; 			# Acceleration due to gravity in m/s2
z1 = 100.; 			# Initial elevation in m

# Calculation
V = math.sqrt(((2*g*z1)+(V1)**2)); 			# Final velocity in m/s2

# Results
print "The velocity of the object just before ir hits the ground is %.1f m/s"%V

# note : incorrect answer in the textbook
The velocity of the object just before ir hits the ground is 109.4 m/s

Example 3.2 Page No : 57

In [1]:
# Variables
dV = 0.5; 			# Change in volume in m3
P = 101.325e03; 			# Atmospheric pressure in N/m2

# Calculation
Wd = P*dV; 			# Work done in J

# Results
print "The amount of work done upon the atmosphere by the ballon is %.2f kJ"%(Wd/1000)
The amount of work done upon the atmosphere by the ballon is 50.66 kJ

Example 3.3 Page No : 58

In [4]:
# Variables
dV = 0.6; 			# Change in volume in m3
P = 101.325e03; 	# Atmospheric pressure in N/m2

# Calculation
Wd = P*dV; 			# Work done in J

# Results
print "The print lacement work done by the air is %.1f KJ"%(Wd/1000)
The print lacement work done by the air is 60.8 KJ

Example 3.4 Page No : 59

In [5]:
import math 

# Variables
T = 1.275e-03; 			# Torque acting against the fluid in N
N = 10000.; 			# Number of revolutions
W1 = 2*math.pi*T*N; 			# Work done by stirring device upon the system
P = 101.325e03; 			# Atmospheric pressure in N/m2
d = 0.6; 			# Piston diameter in m

# Calculation
A = (math.pi/4.)*(d)**2; 			# Piston area in m
L = 0.80; 			        # Displacement of diameter in m
W2 = (P*A*L)/1000.; 			# Work done by the system on the surroundings i KJ
W = -W1+W2; 			# Net work tranfer for the system

# Results
print "The Net work tranfer for the system is %.1f KJ"%W
The Net work tranfer for the system is -57.2 KJ

Example 3.5 Page No : 59

In [2]:
import math 

# Variables
ad = 5.5e-04; 			# Area of indicator diagram
ld = 0.06; 			# Length of diagram
k = 147e06; 			# Spring consmath.tant in MPa/m
w = 150.; 			# Speed of engine
L = 1.2 ; 			# Stroke of piston
d = 0.8; 			# Diameter of the cylinder in m

# Calculation
A = (math.pi/4)*(0.8**2); 			# Area of cylinder
Pm = (ad/ld)*k; 			# Effective pressure
W1 = Pm*L*A*w; 			# Work done in 1 minute
W = (12*W1)/60; 			# The rate of work transfer gas to the piston in MJ/s

# Results
print "The rate of work transfer gas to the piston is %.0f kw"%(round(W/1000,-2))
The rate of work transfer gas to the piston is 24400 kw

Example 3.6 Page No : 60

In [3]:
import math 

# Variables
Tm = 1535.; 			# Melting point of iron on degree
Ti = 15.; 			# Initial temperature
Tf = 1650.; 			# Final temperature
Lh = 270.e03; 			# Latent heat of iron in J/Kg
ml = 29.93; 			# Atomic weight of iron in liquid state
m = 56.; 			# Atomoc weight of iron
sh = 0.502e03; 			# Specific heat of iron in J/Kg
d = 6900.; 			# Density of molten metal in kg/m3

# Calculation and Results
H = (Tm-Ti)*sh + Lh + (ml/m)*(Tf-Tm)*1000; 			# Heat required
Mr = 5e03;      	    		# Melting rate in Kg/h
Hr = H*Mr ; 	    	    	# Rate of heat suppy
HrA = Hr/(0.7*3600) 			# Actual rate of heat supply
print "Rating of furnace would be %.2e"%HrA,"W"

V = (3*Mr)/d;                   			# Volume required in m3
d = ((V/2.)*(4/math.pi))**(1./3); 			# Diameter of cylinder of furnace in m
l = 2*d; 			                        # Length of cylinder of furnace in m
print " Length of cylinder of furnace is %.2f m"%l

# rounding off error.
Rating of furnace would be 2.17e+06 W
 Length of cylinder of furnace is 2.23 m

Example 3.7 Page No : 61

In [18]:
# Variables
SH = 0.9;   			# Specific heat of alluminium in solid state 
L = 390.; 	    		# Latent heat
aw = 27.; 		    	# Atomic weight
D = 2400.; 			    # Density in molten state
Tf = 700.+273; 			# Final temperature
Tm = 660.+273; 			# Melting point of aluminium
Ti = 15.+273; 			# Intial temperature

# Calculation
HR = round(SH*(Tm-Ti)+L+(29.93/27)*(Tf-Tm),1); 			# Heat requires
HS = round(HR/0.7,1) ; 			# Heat supplied
RM = 217*1000*3600/HS ; 			# From the data of problem 3.7
V = 2.18; 			# Volume
M = V*D;

# Results
print "Mass of alluminium that can be melted is %.2f"%(M/1000),"tonnes"
print "Rate at which alluminium can be melted is %.2f"%(RM/100000),"tonnes/h"
Mass of alluminium that can be melted is 5.23 tonnes
Rate at which alluminium can be melted is 5.39 tonnes/h

Example 3.8 Page No : 61

In [9]:
import math 

# Variables
dd = 60e-06;
mw = 1.;
st = 0.07;
dw = 1000.;
dp = 15e-03;

# Calculation
N = (mw*6)/(math.pi*dd**3*dw);
Af = math.pi*dd**2*N;
S_L = 4/(dp*dw);
W = st*(100-S_L);

# Results
print "Work done during automization is %.2f J"%W
Work done during automization is 6.98 J

Example 3.9 Page No : 62

In [20]:
import math 

# Variables
dc = 40e-02;
L = 30e-02;
P = 1e05; 			# Pressure in Pascal
I = 0.5;
V = 24.;
t = 15.*60; 			# in seconds

# Calculation
Wm = V*I*t;
Ws = 0.9*Wm;
W = P*(math.pi/4)*dc**2*L;

# Results
print "Work input to the motor is %.1f kJ"%(Wm/1000)
print "Work input to the stirrer is %.2f kJ"%(Ws/1000)
print "Work done by the fluid on the atmosphere is %.2f kJ"%(W/1000)
Work input to the motor is 10.8 kJ
Work input to the stirrer is 9.72 kJ
Work done by the fluid on the atmosphere is 3.77 kJ

Example 3.10 Page No : 63

In [10]:
import math 

# Variables
P1 = 100.
P2 = 37.9
P3 = 14.4;
V1 = 0.1
V2 = 0.2
V3 = 0.4;

# Calculation
n1 = (math.log(P1/P2))/(math.log(V2/V1));
n2 = (math.log(P2/P3))/(math.log(V3/V2));
# n1 = n2
W = ((P1*V1)-(P3*V3))/(n1-1);

# Results
print "Work done by the system is %.1f kJ"%W
Work done by the system is 10.6 kJ

Example 3.11 Page No : 63

In [25]:
# Variables
P1 = 20*1.01325e05;
V1 = 0.04
V2 = 2*V1;
n = 1.45;

# Calculation
P2 = round((V1/V2)**n*P1,-2)
W12 = ((P1*V1)-(P2*V2))/(n-1);
W23 = P2*(V2-V1);
Wc = W12-W23;

# Results
print "Work done in the cycle is %.2f kJ"%(Wc/1000)

# rounding off error. please check using calculator.
Work done in the cycle is 18.61 kJ