1 liter dry air at STP expands adiabatically to a volume of 3L. If `gamma=1.4`, the work done by air is (`3^(1.4)`= 4.655) (Take air to be an ideal gas)

Options

A. 18J
B. 45J
C. 90.5J
D. 100.8J

Answer

C

Explanation

STP means `P_(1)= 1` atm, T= 273K and `V_(1)=1L`
After adiabatic expansion, `P_(2)=? And V_(2)= 3L`
For adiabatic expansion
`P_(1)V_(1)^(gamma) = P_(2) V_(2)^(gamma)` [ `:.T` is constant]
`:. P_(2) = P_(1) ((V_(1))/(V_(2)))^(gamma)`
`=1 ((1)/(3))^(gamma)`
`=((1)/(3))^(1.4) [ :. gamma= 1.4]`
`= (1)/(3^(1.4))= (1)/(4.655)`
= 0.2148 atm
Work done in adiabatic process, `W= (P_(1)V_(1)- P_(2)V_(2))/(gamma-1)`
`=(1 xx 1-0.2148 xx 3)/(1.4-1)`
`=(1-0.6444)/(0.4)`
`=(0.3556)/(0.4)`
`W= 0.889 xx 1.01 xx 10^(5) xx 10^(-3)J` 91 atm = `1.01 xx 10^(5) (N)/(m^(2)) 1L= 10^(-3) m^(3)`]
`:. W= 0.89789xx 10^(2)J`
`:. W= 89.789J`
`:. W= 90J`