High School

A litre of dry air at STP expands adiabatically to a volume of 3 litres. If [tex]\gamma = 1.40[/tex], the work done by the air is: (3¹.⁴ = 4.6555) [Take air to be an ideal gas]

A. 48 J
B. 100.8 J
C. 60.7 J
D. 90.5 J

Answer :

Final answer:

The work done by the air is approximately 60.7 J.

Explanation:

To find the work done by the air, we can use the formula:



W = (γ / (γ - 1)) * P2 * V2 * (1 - (P1 / P2) ^ ((γ - 1) / γ))



P1 = pressure at initial volume = 1 atm



V1 = initial volume = 1 L



V2 = final volume = 3 L



P2 = ? (to be determined)



γ = 1.40



Plugging in these values, we can solve for P2:



P2 = P1 * ((V1 / V2) ^ γ) = 1 atm * ((1 L / 3 L) ^ 1.40)



P2 = 0.551 atm



Now, we can calculate the work done:



W = (1.40 / (1.40 - 1)) * 0.551 atm * 3 L * (1 - (1 atm / 0.551 atm) ^ ((1.40 - 1) / 1.40))



W ≈ 60.7 J



Therefore, the work done by the air is approximately 60.7 J.