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An adiabatic turbine operates with air entering at 550 kPa, 425 K and 150 m/s and leaving at 110 kPa, 325 K and 50 m/s and T0 = 25 °C.
The actual work production (in kJ/kg) for this turbine, is______. (Answer up to one decimal place)
Correct answer is '111.1'. Can you explain this answer?
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An adiabatic turbine operates with air entering at 550 kPa, 425 K and...
Given data:
- Inlet conditions:
- Pressure (P1): 550 kPa
- Temperature (T1): 425 K
- Velocity (V1): 150 m/s
- Outlet conditions:
- Pressure (P2): 110 kPa
- Temperature (T2): 325 K
- Velocity (V2): 50 m/s
- Ambient temperature (T0): 25 °C
Assumptions:
- The turbine operates adiabatically, meaning no heat is transferred to or from the surroundings.
- The turbine is frictionless, so there are no losses due to friction.
- The air behaves as an ideal gas.
Approach:
To calculate the actual work production of the turbine, we need to consider the changes in kinetic energy, potential energy, and internal energy of the air.
Calculations:
1. Change in kinetic energy (ΔKE):
- KE1 = 0.5 * m * V1^2 (initial kinetic energy)
- KE2 = 0.5 * m * V2^2 (final kinetic energy)
- ΔKE = KE2 - KE1
2. Change in potential energy (ΔPE):
- PE1 = 0 (since the reference level is not given)
- PE2 = 0 (since the reference level is not given)
- ΔPE = PE2 - PE1 = 0 - 0 = 0
3. Change in internal energy (ΔU):
- U1 = m * u1 (initial internal energy)
- U2 = m * u2 (final internal energy)
- ΔU = U2 - U1
4. Heat transfer (Q):
- Q = 0 (adiabatic process)
5. Work transfer (W):
- W = Q + ΔKE + ΔPE + ΔU (from the first law of thermodynamics)
Calculations using ideal gas equations:
1. Mass flow rate (m):
- m = P1 * A1 / (R * T1) (using ideal gas equation)
2. Specific gas constant (R):
- R = R_air / M (where R_air is the universal gas constant for air and M is the molar mass of air)
3. Inlet area (A1):
- A1 = π * d1^2 / 4 (assuming the inlet is circular)
4. Inlet and outlet densities (ρ1 and ρ2):
- ρ1 = P1 / (R * T1)
- ρ2 = P2 / (R * T2)
5. Specific enthalpy (h):
- h1 = h0 + C * T1 (using the definition of specific enthalpy, where h0 is the specific enthalpy at T0 and C is the specific heat capacity at constant pressure)
- h2 = h0 + C * T2
6. Specific internal energy (u):
- u1 = h1 - P1 / ρ1 (using the definition of specific internal energy)
- u2 = h2 - P2 / ρ2
7. Work transfer per unit mass (w):
- Inlet conditions:
- Pressure (P1): 550 kPa
- Temperature (T1): 425 K
- Velocity (V1): 150 m/s
- Outlet conditions:
- Pressure (P2): 110 kPa
- Temperature (T2): 325 K
- Velocity (V2): 50 m/s
- Ambient temperature (T0): 25 °C
Assumptions:
- The turbine operates adiabatically, meaning no heat is transferred to or from the surroundings.
- The turbine is frictionless, so there are no losses due to friction.
- The air behaves as an ideal gas.
Approach:
To calculate the actual work production of the turbine, we need to consider the changes in kinetic energy, potential energy, and internal energy of the air.
Calculations:
1. Change in kinetic energy (ΔKE):
- KE1 = 0.5 * m * V1^2 (initial kinetic energy)
- KE2 = 0.5 * m * V2^2 (final kinetic energy)
- ΔKE = KE2 - KE1
2. Change in potential energy (ΔPE):
- PE1 = 0 (since the reference level is not given)
- PE2 = 0 (since the reference level is not given)
- ΔPE = PE2 - PE1 = 0 - 0 = 0
3. Change in internal energy (ΔU):
- U1 = m * u1 (initial internal energy)
- U2 = m * u2 (final internal energy)
- ΔU = U2 - U1
4. Heat transfer (Q):
- Q = 0 (adiabatic process)
5. Work transfer (W):
- W = Q + ΔKE + ΔPE + ΔU (from the first law of thermodynamics)
Calculations using ideal gas equations:
1. Mass flow rate (m):
- m = P1 * A1 / (R * T1) (using ideal gas equation)
2. Specific gas constant (R):
- R = R_air / M (where R_air is the universal gas constant for air and M is the molar mass of air)
3. Inlet area (A1):
- A1 = π * d1^2 / 4 (assuming the inlet is circular)
4. Inlet and outlet densities (ρ1 and ρ2):
- ρ1 = P1 / (R * T1)
- ρ2 = P2 / (R * T2)
5. Specific enthalpy (h):
- h1 = h0 + C * T1 (using the definition of specific enthalpy, where h0 is the specific enthalpy at T0 and C is the specific heat capacity at constant pressure)
- h2 = h0 + C * T2
6. Specific internal energy (u):
- u1 = h1 - P1 / ρ1 (using the definition of specific internal energy)
- u2 = h2 - P2 / ρ2
7. Work transfer per unit mass (w):
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An adiabatic turbine operates with air entering at 550 kPa, 425 K and 150 m/s and leaving at 110 kPa, 325 K and 50 m/s and T0 = 25 °C.The actual work production (in kJ/kg) for this turbine, is______. (Answer up to one decimal place)Correct answer is '111.1'. Can you explain this answer?
Question Description
An adiabatic turbine operates with air entering at 550 kPa, 425 K and 150 m/s and leaving at 110 kPa, 325 K and 50 m/s and T0 = 25 °C.The actual work production (in kJ/kg) for this turbine, is______. (Answer up to one decimal place)Correct answer is '111.1'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about An adiabatic turbine operates with air entering at 550 kPa, 425 K and 150 m/s and leaving at 110 kPa, 325 K and 50 m/s and T0 = 25 °C.The actual work production (in kJ/kg) for this turbine, is______. (Answer up to one decimal place)Correct answer is '111.1'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An adiabatic turbine operates with air entering at 550 kPa, 425 K and 150 m/s and leaving at 110 kPa, 325 K and 50 m/s and T0 = 25 °C.The actual work production (in kJ/kg) for this turbine, is______. (Answer up to one decimal place)Correct answer is '111.1'. Can you explain this answer?.
An adiabatic turbine operates with air entering at 550 kPa, 425 K and 150 m/s and leaving at 110 kPa, 325 K and 50 m/s and T0 = 25 °C.The actual work production (in kJ/kg) for this turbine, is______. (Answer up to one decimal place)Correct answer is '111.1'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about An adiabatic turbine operates with air entering at 550 kPa, 425 K and 150 m/s and leaving at 110 kPa, 325 K and 50 m/s and T0 = 25 °C.The actual work production (in kJ/kg) for this turbine, is______. (Answer up to one decimal place)Correct answer is '111.1'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An adiabatic turbine operates with air entering at 550 kPa, 425 K and 150 m/s and leaving at 110 kPa, 325 K and 50 m/s and T0 = 25 °C.The actual work production (in kJ/kg) for this turbine, is______. (Answer up to one decimal place)Correct answer is '111.1'. Can you explain this answer?.
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