KVPY SB SX Exam 2011 Question Paper

Question : 27 of 120

Marks: +1, -0

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:

a heater to warm the air injected into the cabin
an air-conditioner to cool the air injected into the cabin
neither a heater nor an air-conditioner; the compressor is sufficient
alternatively heating and cooling in the two halves of the compressor cycle

Validate

Solution:

\PV^\γ=C

\P^{1-\γ}=C

(0.28)^{1-\γ}×(233)^{\γ}=1^{1-\γ}×T^{\γ}

\γ=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}

T is coming more than 298 K or 25ºC
∴ T is more than 25°C
so to cool it an extra ac is required.

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