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A steam turbine receives steam steadily at 10 bar with an enthalpy of 3000kJ/kg and discharges at 1 bar with an enthalpy of 2700 kJ/kg. The workoutput is 250 kJ/kg. The changes in kinetic and potential energies are negligible. The heat transfer from the turbine casing to the surroundingsis equal to 
  • a)
    0 kJ
  • b)
    50 kJ
  • c)
    150 kJ
  • d)
    250 kJ
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A steam turbine receives steam steadily at 10 bar with an enthalpy of ...
 Enthalpy drop = Power output + losses Or 3000 – 2700 = 250 + losses Or losses = 50 kJ to the surrounding
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A steam turbine receives steam steadily at 10 bar with an enthalpy of ...
Given:
- Steam enters the turbine at a pressure of 10 bar with an enthalpy of 3000 kJ/kg.
- Steam is discharged from the turbine at a pressure of 1 bar with an enthalpy of 2700 kJ/kg.
- Work output of the turbine is 250 kJ/kg.
- Changes in kinetic and potential energies are negligible.

To find:
The heat transfer from the turbine casing to the surroundings.

Explanation:

1. Specific Enthalpy:
Enthalpy is the sum of internal energy and flow energy. It represents the total heat energy of a substance. The specific enthalpy is the enthalpy per unit mass of the substance.

Given:
- Specific enthalpy at turbine inlet (h1) = 3000 kJ/kg
- Specific enthalpy at turbine outlet (h2) = 2700 kJ/kg

2. Work Output:
Work output of the turbine is the energy transferred out of the system in the form of mechanical work.

Given:
- Work output (W) = 250 kJ/kg

3. Heat Transfer:
Heat transfer represents the energy exchanged between the turbine casing and the surroundings.

The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.

Mathematically,
ΔU = Q - W

Since there are no changes in kinetic and potential energies, the change in internal energy (ΔU) is zero.

Therefore,
0 = Q - W
=> Q = W

In this case, the heat transfer from the turbine casing to the surroundings is equal to the work output of the turbine.

Given:
- Heat transfer (Q) = Work output (W) = 250 kJ/kg

4. Conclusion:
The heat transfer from the turbine casing to the surroundings is 250 kJ/kg, which is equal to the work output of the turbine.

Answer:
The correct answer is option B) 50 kJ.
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A steam turbine receives steam steadily at 10 bar with an enthalpy of 3000kJ/kg and discharges at 1 bar with an enthalpy of 2700 kJ/kg. The workoutput is 250 kJ/kg. The changes in kinetic and potential energies are negligible. The heat transfer from the turbine casing to the surroundingsis equal toa)0 kJb)50 kJc)150 kJd)250 kJCorrect answer is option 'B'. Can you explain this answer?
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