Question

Q1:A 3.70 -molesample of a perfect gas with CP,m= 17.5 JK-1mol-1is initially at 50 oCand 1.75 x 103Pa. The sample undergoes a reversible adiabatic expansion until its temperature reaches 65 oC. Determine:

a.The initial and final volumes

b.The heat (q), work (w), internal energy change (ΔU) and enthalpy change (ΔH)

Answer 1

Step I

Moles of sample gas = 3.7

C_p,m = 17.5 J/K-mol

T_i = 50 ^oC T_f = 65 ^oC

P_i = 180.25 Pa

Step II

a) Initial Volume, V_i = nRT_i / P_i = (3.7 x 0.0821 x 323.15) / (180.25/101325) = 55181 lit

b) For adiabatic expansion,

Cp - Cv = R

= Cp / Cv = Cp / (Cp - R) = 17.5 / (17.5 - 8.314) = 1.905

Substituting the values we get,

P_f = 198.314 Pa

V_f = nRT_f / P_f = (3.7 x 0.0821 x 338.15) / (198.314/101325) = 52482.86 lit

b) For adiabatic process, Heat (q) = 0

Work (w) = Internal energy change (delta U)

After putting the values we get, W = - 510 J