Chapter 4.8, Problem 15P
Interpretation:
The value of entropy and the process is possible or not.
Concept Introduction:
Theentropy balance equation for the turbine.
M2S_2−M1S_1=minS_in−moutS_out+QT+Sgen
Here, total mass of container 2 is M2, molar entropy of container 2 is S_2, total mass of container 1 is M1, molar entropy of container 1 is S_1, initial mass is min, initial molar entropy is S_in, final mass is mout, final molar entropy is S_out, temperature is T, heat is added or removed from the system is Q, and entropy is generated within the boundaries of the system is Sgen.
Thesteady state energy balance equation for the turbine.
ddt{M(U^+V22+gh)}=[min(H^in+Vin22+ghin)−mout(H^out+Vout22+ghout)+WS+WEC+Q]
Here, time taken is t, total mass is M, specific internal energy is U^, velocity is V, acceleration due to gravity is g, height is h, initial mass flow is min, initial specific enthalpy is H^in, initial velocity is Vin, initial height of the gas is hin, final mass flow is mout, final height of the gas is hout, shaft work is added to the system is WS, and work is added to the system through expansion or contraction of the system is WEC.
The ideal gas equation.
PV=nRT
Here, number of mole is n, gas constant is R, temperature is T1, and pressure is P.
The expression to determine the net molar entropy (S_2−S_1).
S_2−S_1=CV∗ln(T2T1)+Rln(RT2/P2RT1/P1)=CV∗ln(T2T1)+Rln(T2P1T1P2)
Here, final temperature is T2, final pressure is P2,initial temperature is T1, and initial pressure is P1.