Interpretation:
The discharge temperature of isobutene and the power output of the turbine under the given conditions need to be calculated
Concept Introduction:
- For an ideal gas under isentropic adiabatic conditions, the temperature and pressure are related as:
- The isentropic efficiency of a turbine is given as:
The discharge temperature of isobutane =
Power output of turbine = -4250 kW
Given Information:
Inlet pressure, P1 = 5000 kPa
Inlet Temperature, T1=
Outlet pressure, P2 = 500 kPa
Molar flow rate = 0.7 kmol/s
Turbine efficiency, ? = 0.80
Explanation:
In this case, isobutane has been assumed to behave as an ideal gas. The discharge temperature can be deduced from equation (1) and the power output can be deduced from equation (4).
The heat capacity ratio for isobutane, i.e. ? = 1.2
Calculation:
Step 1:
Calculate the discharge/final temperature, T2
Based on equation (1) we have:
Step 2:
Calculate the actual enthalpy change
The adiabatic enthalpy change is related to the change in temperature through the specific heat capacity, Cp
Based on equation (5) the actual enthalpy change is:-
Step 3:
Calculate the power output of the turbine
Based on equation (4)
Thus, the discharge temperature of isobutane =
Power output of turbine = -4250 kW
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