# Chapter 2 : Basic Thermodynamics¶

### Example 2.1 Page: 27¶

In [4]:

import math

# Variables
m = 1.          #[lbm] Mass of the steam
T_1 = 300.      #[F] Initial temperature
P_1 = 14.7      #[psia] Initial pressure
P_sorronding = 14.7     #[psia]
Q = 50.         #[Btu] Amount of the energy added to the system as heat

# This is a closed system and we can apply the following equations
# delta_U_system = sum(dQ_in_minus_out) + sum(dW_in_minus_out)                                (A)
# dS_system = (m*ds)_system = sum((dQ)/T)_in_minus_out + dS_reversible                        (B)

# From the steam tables, we look up the properties of steam at temperature 300F and pressure 14.7 psia and find
u_initial = 1109.6      #[Btu/lbm] Internal energy of the steam
h_initial = 1192.6      #[Btu/lbm] Enthalpy of the steam
s_initial = 1.8157      #[Btu/(lbm*R)] Entropy of the steam

# The work here is done by the system, equal to
#  -delta_w = P*A_piston*delta_x = P*m*delta_v

# Calculations
# Substituting this in the equation (A) and rearranging, we have
#  m*delta_(u + P*v) = m*delta_h = delta_Q
# From which we can solve for the final specific enthalpy
h_final = h_initial + Q     #[Btu/lbm]

# Now, by the linear interpolation we find that at h = 1242.6 Btu/lbm and P = 1 atm, temperature of the steam is given
T_2 = 405.7                 #[F] Final temperature

# At this final temperature and pressure we have the steam properties
u_final = 1147.7            #[Btu/lbm]
s_final = 1.8772            #[Btu/(lbm*R)]

# Thus, increase in the internal energy, enthalpy and entropy are
delta_u = u_final - u_initial       #[Btu/lbm]
delta_s = s_final - s_initial       #[Btu/(lbm*R)]
delta_h = Q                         #[Btu/lbm]

# The work done on the atmosphere is given by
w = delta_h - delta_u               #[Btulbm]

# Results
print "The increase in internal energy of the steam by adding the heat is %0.2f Btu/lbm"%(delta_u)
print "The increase in enthalpy of the steam by adding the heat is        %0.2f Btu/lbm"%(delta_h)
print "The increase in entropy of the steam by adding the heat is         %0.4f Btu/lbm"%(delta_s)
print "Work done by the piston expanding against the atmosphere is       %0.2f Btu/lbm"%(w)

The increase in internal energy of the steam by adding the heat is 38.10 Btu/lbm
The increase in enthalpy of the steam by adding the heat is        50.00 Btu/lbm
The increase in entropy of the steam by adding the heat is         0.0615 Btu/lbm
Work done by the piston expanding against the atmosphere is       11.90 Btu/lbm


### Example 2.2 Page: 28¶

In [1]:

import math

# Variables
T_in = 600.      #[F] Input steam temperature
P_in = 200.      #[psia] Input steam pressure
P_exit = 50.     #[psia]

# (work per pound) = W/m = -( h_in - h_out )

# From the steam table we can read the the inlet enthalpy and entropy as
h_in = 1322.1       #[Btu/lbm]
s_in = 1.6767       #[Btu/(lb*R)]

# Now, we need the value of h_out

# sum(s*m_in_minus_out) = ( s_in - s_out ) = 0

# Which indicates that inlet and outlet entropies are same
# We can find the outlet temperature by finding the value of the temperature in the steam table
# For which the inlet entropy at 50 psia is the same as the inlet entropy, 1.6767 Btu/(lb*R).
# By linear interpolation in the table we find
T_in = 307.1        #[R]

# and by the linear interpolation in the same table we find that
h_out = 1188.1      #[Btu/lb]

# Calculations
# Thus, we find
W_per_pound = (h_in - h_out)       #[Btu/lb]

# Results
print " The work output of the turbine of steam is %0.1f Btu/lb"%(-W_per_pound)

 The work output of the turbine of steam is -134.0 Btu/lb


### Example 2.3 Page: 38¶

In [6]:

import math

# Variables
T = 500.        #[F]
P = 680.        #[psi]

# Calculations
# It is reported in the book in the table A.1(page 417) that for water
# We know that T_r = T/T_c and P_r = P/P_c, so
T_c = 647.1*1.8     #[R]
P_c = 220.55*14.51  #[psia]
w = 0.345
T_r = (T+459.67)/T_c
P_r = P/P_c
z_0 = 1+P_r/T_r*(0.083-0.422/T_r**(1.6))
z_1 = P_r/T_r*(0.139-0.172/T_r**(4.2))
z = z_0+w*z_1

# Results
print "The compressibility factor of steam at the given state is %0.3f"%(z)
# Based on the steam table (which may be considered as reliable as the experimental data, the value of z is 0.804.

The compressibility factor of steam at the given state is 0.851

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