5.1: Energy balance for Stream in Control Volume#
Problem statement:#
a) the pressure reading on a pressure gauge at atmospheric pressure
The steam is then heated to double the pressure while the volume does not change. Determine the following:
b) the temperature of steam after heating
c) how much heat is require to do this
d) how would this change if if
Solution Approach for a)#
Density
#importing the required library
import CoolProp.CoolProp as CP
# define the given inputs:
T = 400 + 273.15 #temperature in K
D = 1 / 1 #density in kg/m3
P = CP.PropsSI('P', 'D', D, 'T', T, 'Water') #calculating pressure using coolprop Pa
P_g = P - 101325 #gauge pressure in Pa
print('The gauge pressure of steam at the given initial properties is',f"{P_g:.1f}",'Pa')
The gauge pressure of steam at the given initial properties is 208099.6 Pa
Solution Approach for b)#
The known parameters from the secondary state are pressure
and density
since the mass and the volume of the space remains constant
# define the inputs:
P_g2 = P_g * 2 #gauge pressure in secondary state in Pa
P_2 = P_g2 + 101325 #absolute pressure in secondary state in Pa
D_2 = D #density in the secondary state in kg/m3
T_2 = CP.PropsSI('T', 'D', D_2, 'P', P_2, 'Water') #calculating secondary temperature using coolprop in K
T_2C = T_2 - 273.15 #temperature at secondary state in C
print('The temperature of steam at the secondary state is',f"{T_2C:.1f}",'C')
The temperature of steam at the secondary state is 849.0 C
Solution Approach for c)#
Given the first law of thermodynamics,
and
# define the inputs using coolprop:
m = 1 #steam mass in kg
u_1 = CP.PropsSI('U', 'D', D, 'T', T, 'Water') #calculating initial internal energy in J/kg
u_2 = CP.PropsSI('U', 'D', D_2, 'P', P_2, 'Water') #calculating secondary internal energy in J/kg
Q = m * (u_2 - u_1) / 1000 #heat required in kJ
print('The heat required to double the gauge presure is',f"{Q:.1f}",'kJ')
The heat required to double the gauge presure is 790.8 kJ
Solution Approach for d)#
To use
#define the constants
C_v = 1.4108 #C_v of steam in kJ/kg.k
Q = m * C_v * (T_2 - T) #heat required in kJ
print('The heat required to double the gauge presure is',f"{Q:.1f}",'kJ','using C_v')
The heat required to double the gauge presure is 633.5 kJ using C_v