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

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

B

Explanation

`PV^(gamma)=C`
`P^(1-gamma)T^(gamma)=C`
`(0.28)^(1-gamma)xx(233)^(gamma)=1^(1-gamma)xxT^(gamma) implies gamma=7/5`
`(0.28)^(1-7//5)xx(233)^(7//5)=1^(1-7//5)xxT^(7//5)`
`T^(7//5)=233^(7//5)xx(0.28)^(-2//5), T=233(0.28)^(-2//7)`
`T=(233)/((0.28)^(2//7))`, T is coming
More than 298K or `25^@C`
`:.` T is more than `25^@C`
So to cool it, an extra AC is required.