Five moles of monatomic ideal gas have initial pressure 2.50 * 103 Pa and initial volume 2.10 m3. While undergoing an adiabatic expansion, the gas does 1480 J of work. What is the final pressure of the gas after the expansion?

Question

Micah Cabrera

Chemistry

18 August, 22:42

Five moles of monatomic ideal gas have initial pressure 2.50 * 103 Pa and initial volume 2.10 m3. While undergoing an adiabatic expansion, the gas does 1480 J of work. What is the final pressure of the gas after the expansion?

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Answers (1)

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Ruben Lozano · Answer 1

pressure of the gas after the expansion is 1795.238 Pa

Explanation:

adiabatic expansion W (+) - ideal gas:

Q = 0 ... adiabatic system PV = RTn ... (1) ... ideal gas W = ∫ PdV ... (2) from first law of thermodynamic 1 Pa ≡ J / m³

deriving (1):

⇒ PdV + VdP = RndT

⇒ PdV = RndT - VdP

being the T constant ⇒ dT = 0

⇒ PdV = - VdP ... (3)

(3) in (1):

⇒ W = ∫ ( - VdP)

⇒ W = - V ∫dP

⇒ W = - V * (P2 - P1)

⇒ P2 = - (W / V) + P1

⇒ P2 = - (1480 J / 2,1 m³) + 2.5 E3 J / m³

⇒ P2 = - 704.762 J/m³ + 2.5 E3 J/m³

⇒ P2 = 1795.238 Pa