Initial pressure and volume of a monoatomic ideal gas are P and V . The change in internal energy of this gas in adiabatic expansion to volume V_ final =27V is ________ J.

Step-by-step solution

For a monoatomic ideal gas, the ratio of specific heats is = 5 3 . In an adiabatic process, PV^ = constant . P₁ V₁^ = P₂ V₂^ P V^ 5/3 = P₂ (27V)^ 5/3 P₂ = P ( 1 27 )^ 5/3 = P 243 The change in internal energy is given by: U = P₂ V₂ - P₁ V₁ - 1 Substituting the values: U = ( P 243 )(27V) - PV 5 3 - 1 U = PV 9 - PV 2 3 U = - 8 9 PV 2 3 = - 4 3 PV Answer: - 4 3 PV