Question

Two moles of ideal diatomic gas ( Cv = 5/2 R ) at 300 k and 5 atm expanded irreversibly and adiabatically to a final pressure of 2 atm against a contant pressure of 1 atm.
calculate q , w, delta h and delta U

Answer 1

The value of q, w, ΔH and ΔU are:

• 2 moles of ideal diatomic gas at 300 K and 5 atm is expanded irreversibly and adiabatically to a final pressure of 2 atm against a constant pressure of 1 atm.
• Given, $P_{ext}$ = 1 atm

                   P₁ = 5 atm      T₁ = 300 K

                   P₂ = 2 atm      T₂ = T = ?

                   n = 2

                   $C_v$ = 2.5 R

• For adiabatic process, q=0.
• For an adiabatic process,  W = n$C_v$ dT= −PΔV

                                         ⇒ n  $C_v$ ( T₂ - T₁ ) = - P ( V₂ - V₁ )

                                         ⇒ n  $C_v$ ( T₂ - T₁ ) = - P n R ( (T₂/P₂) - (T₁/P₁))

        Putting the values and solving it, we get : T₂ = T = 270 K

• W = n$C_v$ dT = -1247.1 J
• ΔU = W = -1247.1 J

• ΔH = ΔU + n R ΔT = − 1745.94 J