Question

Two moles of a perfect gas undergo the following processes : 

(a) a reversible isobaric expansion from (1.0 atm, 20.0 L) to (1.0 atm, 40.0 L) 

(b) a reversible isochoric change of state from (1.0 atm, 40.0 L) to (0.5 atm,40.0 L) 

(c) a reversible isothermal compression from (0.5 atm, 40.0 L) to (1.0 atm. 20.0 L) 

(i) Sketch with labels each of the processes on the same p-V diagram. 

(ii) Calculate the total work (W) and the total heat change (Q) involved in the above processes. 

(iii) What will be the values of ΔU, ΔH and ΔS for the overall process ?

Answer 1

(i) p-V diagram

(a) In reversible isobaric expansion pressure is constant (ie, 1.0 atm) and volume is increased from 20.0 L to 40.0 L (from state 1 to 2). So work done 

(w₁) = - p(V₂ - V₁) 

= -1 x (40 - 20)

= - 20 L-atm 

(b) In reversible isochoric change of state (from '2' to 3), volume is constant (40 L) while pressure is decreased from 1 atm to 0.5 atm. Hence, in this change work done(W₂) = 0 

(c) In reversible isothermal compression volume and pressure both are change. Thus system is reached at state 'I' (Change takes place from 3 to 1). Hence, in this change work done 

W₃ = - 2.303 nRT log₁₀ V₂/V₁