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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?

Respuesta :

Answer:

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

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