Answer:
a) -207.793 KJ/Kg
b) 0.08 [KJ/kg.K]
c) 0.808
Step-by-step explanation:
Given
Temperature at state 1 T_1 = 300 K
Temperature at state 2 T_2 = 520 K
Pressure at state 1 P_1 = 1 bar
Pressure at state 2 P_2 = 10 bar
Required
The specific work input [KJ/kg]
The rate of entropy production [KJ/kg.K]
The isentropic compressor efficiency.
Assumption
Carbon dioxide in a compressor assembly is compressed adiabatically . The steam is a closed system.
Applying the ideal gas model.
Kinetic energy effects can be neglected.
Potential energy effects can be neglected.
Solution
Specific entropy at state 1 from Table A-3 at T_1 = 300 K and P_1 = 1 bar
s_1 = 5.3754 [KJ/kg.K]
Specific entropy at state 2 from Table A-3 at T2 = 520 K and P_2 = 10 bar
s_2 = 4.860 [KJ/kg.K]
The rate of entropy production could be defined as following.
σ/m = s°(T_2) - s°(T_1) - R*ln(P_2/P_1)
(5.3754-4.860)-(8.314/44.01)*ln(10/1)
= 0.08 [KJ/kg.K]
Energy equation at compressor for actual process could be defined as following.
Q-W = m [(h_2-h_1)+(V_2^2- V_1^2)/2 + g(Z_2-Z_1)]
As stray heat transfer is neglected at compressor.
-W = m [(h_2-h_1)+(V_2^2- V_1^2)/2 + g(Z_2-Z_1)]
Potential energy play can be neglected.
-W = m [(h_2-h_1)+(V_2^2- V_1^2)/2 ]
Kinetic energy play can be neglected.
-W = m [(h_2-h_1)]
The work of compressor for actual process could be defined as following.
W/m(turbine) = -(h_2-h_1)
214.2922-422.08588 = -207.793 KJ/Kg
Energy equation at compressor for ideal process could be defined as following.
Q-W = m [(h_2s-h_1)+(V_2s^2- V_1^2)/2 + g(Z_2s-Z_1)]
As stray heat transfer is neglected at compressor.
-W = m [(h_2s-h_1)+(V_2s^2- V_1^2)/2 + g(Z_2s-Z_1)]
Potential energy play can be neglected.
-W = m [(h_2s-h_1)+(V_2s^2- V_1^2)/2]
Kinetic energy play can be neglected.
-W = m [(h_2s-h_1)
The specific work of compressor for ideal process could be defined as following.
W/m(turbine ideal) = -(h_2s-h_1)
For the isentropic process.
P_2/P_1 = P_r*(T_2)/P_r*(T_1)
The relative pressure for air at state 1 from table A-22 at T_1 = 290 K
P_r*(T_1)=2.2311
The relative pressure for air at state 2 could be defined as following.
P_r*(T_2) = P_r*(T_1)*P_2/P_1
= 4.52
The specific enthalpy at state 2s could be defined as following by Interpolation using Table A-22 at Pr(T_2) = 4.062
h_2s = 382.1402 KJ/Kg
The isentropic compressor efficiency could be defined as following.
η_(turbine) = W_(ideal)/W_(act)
= (h_1-h_2s)/ (h_1-h_2)
= 0.808