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KVPY2011PhysicsKinetic Theory of Gases

Jet aircrafts fly at altitudes above 30,000 ft where the air is very cold at -40^ C and the pressure is 0.28 ~atm . The cabin is maintained at 1 atm pressure by means of a compressor which exchanges air from outside adiabatically. In order to have a comfortable cabin temperature of 25^ C , we will require in addition -

Options

  1. Aa heater to warm the air injected into the cabin
  2. Ban air-conditioner to cool the air injected into the cabin
  3. Cneither a heater nor an air-conditioner; the compressor is sufficient
  4. Dalternatively heating and cooling in the two halves of the compressor cycle

Correct answer

B. an air-conditioner to cool the air injected into the cabin

Step-by-step solution

PV ^ = C array l P ^ 1- T ^ = C (0.28)^ 1- (233)^ =1^ 1- T ^ = 7 5 (0.28)^ 1-7 / 5 (233)^ 7 / 5 =1^ 1-7 / 5 T ^ 7 / 5 ~T ^ 7 / 5 =233^ 7 / 5 (0.28)^ -2 / 5 ~T =233(0.28)^ -2 / 7 ~T = 233 (0.28)^ 2 / 7 array T is coming more than 298 ~K or 25^ C T is more than 25^ C so to cool it an extra ac is required.

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