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Alexxandr [17]
3 years ago
7

Air enters a turbine operating at steady state at 8 bar, 1400 K and expands to 0.8 bar. The turbine is well insulated, and kinet

ic and potential energy effects can be neglected. Assuming ideal gas behavior for the air, what is the maximum theoretical work that could be developed by the turbine in kJ per kg of air flow?
Physics
1 answer:
vladimir2022 [97]3 years ago
5 0

To solve this problem it is necessary to apply the concepts related to the adiabatic process that relate the temperature and pressure variables

Mathematically this can be determined as

\frac{T_2}{T_1} = (\frac{P_2}{P_1})^{(\frac{\gamma-1}{\gamma})}

Where

T_1 =Temperature at inlet of turbine

T_2 = Temperature at exit of turbine

P_1 = Pressure at exit of turbine

P_2 =Pressure at exit of turbine

The steady flow Energy equation for an open system is given as follows:

m_i = m_0 = m

m(h_i+\frac{V_i^2}{2}+gZ_i)+Q = m(h_0+\frac{V_0^2}{2}+gZ_0)+W

Where,

m = mass

m_i = mass at inlet

m_0= Mass at outlet

h_i = Enthalpy at inlet

h_0 = Enthalpy at outlet

W = Work done

Q = Heat transferred

V_i = Velocity at inlet

V_0= Velocity at outlet

Z_i= Height at inlet

Z_0= Height at outlet

For the insulated system with neglecting kinetic and potential energy effects

h_i = h_0 + W

W = h_i -h_0

Using the relation T-P we can find the final temperature:

\frac{T_2}{T_1} = (\frac{P_2}{P_1})^{(\frac{\gamma-1}{\gamma})}

\frac{T_2}{1400K} = (\frac{0.8bar}{8nar})^{(\frac{1.4-1}{1.4})}

T_2 = 725.126K

From this point we can find the work done using the value of the specific heat of the air that is 1,005kJ / kgK

So:

W = h_i -h_0

W = C_p (T_1-T_2)

W = 1.005(1400-725.126)

W = 678.248kJ/Kg

Therefore the maximum theoretical work that could be developed by the turbine is 678.248kJ/kg

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