Question

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

• A. A heater to warm the air injected into the cabin
• B. An air-conditioner to cool the air injected into the cabin
• C. Neither a heater nor an air-conditioner: the compressor is sufficient
• D. Alternatively heating and cooling in the two halves of the compressor cycle

Answer 1

The correct option is B An air-conditioner to cool the air injected into the cabin

$\gamma =\frac{7}{5}$

$P^{1-\gamma }{T}^{\gamma }=C$

${0.28}^{1-\gamma }{233}^{\gamma }=1^{1-\gamma }{T}^{\gamma }$

$T=340K$

hence we need to cool the incoming air to 298K