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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.
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