Answer to Question #143659 in Physical Chemistry for Aviana

Question

Five moles of an ideal gas (CV,m = 3R/2) at 240 K and 10 atm (state i) are
compressed adiabatically to 300 K and 20 atm (state f).
(a) Devise a path consisting of two steps, one of which must be an isochoric process, to return to the initial state. Indicate states i and f, and the proposed path on a PV diagram.
(b) Determine q, w, ΔU and ΔH for the proposed path
(c) Deduce if it is possible for the ideal gas to be compressed reversibly and adiabatically from state i to state f.

Answer 1

a)

  

 

 

 

b)

q = 0

ΔU = w = C_V n ΔT = 3/2 R n ΔT = 3/2 x 8.314 x 5 x 60 = 3741.3 J

ΔH = C_p ΔT = 5/2 R Δ T = 5/2 x 8.314 x 60 = 1247.1 J

c)

Let us imagine a situation with a cylinder and a piston. The piston moves very slowly. The volume changes from V_i to V_f. The walls are adiabatic, i.e. there is no heat exchange with the surroundings; consequently dQ = 0. So, the only work involved is that of compression.