Chemistry - Thermodynamics - I Question with Solution | TestHub
ChemistryThermodynamics - IWorkMedium2 minQB
ChemistryMediumnumerical
A balloon containing air at 27°C and 1 bar initially is filled with air further, isothermally and reversibly till the pressure is 4 bar. If the initial diameter of the balloon is 1 m and the pressure at each stage is proportional to diameter of balloon, the magnitude of work done (in 10⁷ J) is
Answer:
1.00
Solution:
P = k·d with k = 1 bar m⁻¹ (P₁ = 1 bar at d₁ = 1 m), so d₂ = 4 m. V = πd³/6 ⇒ dV = (πd²/2) dd. W = ∫P dV = ∫₁⁴ k d·(πd²/2) dd = (kπ/8)(d₂⁴ − d₁⁴) = (10⁵·π/8)(4⁴ − 1⁴) = 10⁵·π·255/8 ≈ 1.0×10⁷ J. In units of 10⁷ J, the answer is 1.
Stream:JEESubject:ChemistryTopic:Thermodynamics - ISubtopic:Work
⏱ 2mℹ️ Source: QB
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