An isentropic air-turbine is used to supply 0.1 kg/s of air at 0.1 MN/m² and 285 K to a cabin. The pressure at the inlet to the turbine is 0.4 MN/m². What will be the power developed by the turbine? [Consider  ]

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  1. 14.25 kW 
  2. 10.25 kW
  3. 6.75 kW
  4. 8.25 kW 

Answer (Detailed Solution Below)

Option 1 : 14.25 kW 
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Detailed Solution

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Concept:

We use isentropic expansion relations in a turbine to determine the power developed when supplying air to a cabin.

Given:

  • Mass flow rate,
  • Inlet pressure,
  • Exit pressure,
  • Exit temperature,
  • Specific heat at constant pressure,
  • Ratio of specific heats,
  • Given relation:

Step 1: Determine the inlet temperature (T₁)

For an isentropic process:

Step 2: Calculate the work output (power)

The power developed by the turbine is given by:

 

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