Chapter 5, Problem 5.32NP

(a)

Interpretation Introduction

Interpretation:

The entropy changes; ΔS_surr and ΔS_totalfor a gas that undergoes reversible adiabatic expansion from an initial temperature of 298 K and 450 bar until the final pressure is 1/3 its initial value needs to be deduced.

Concept Introduction:

The entropy change associated with a reversible process is given as a ratio of the heat transferred (q_rev) at a given temperature T

  $\text{ΔS = }\frac{{\text{q}}_{\text{rev}}}{\text{T}}\text{ -----(1)}$

The total entropy change is given as a sum of the entropy change of the system and surroundings

  ${\text{ΔS = ΔS}}_{\text{system}}{\text{+ΔS}}_{\text{surr}}\text{ ------(2)}$

A given process is spontaneous if the entropy change is positive

i.e. ΔS < 0, spontaneous process

(b)

Interpretation Introduction

Interpretation:

The entropy changes; ΔS_surr and ΔS_total for a gas that undergoes adiabatic expansion from an initial temperature of 298 K and 450 bar against a constant external pressure of 1.50 bar unit the final pressure is 1/3 the initial value needs to be deduced

Concept Introduction:

For an ideal gas, the entropy change associated with anirreversible process from initial pressure and temperature P₁,T₁ to a final state with P₂, T₂ is given as

  $\text{ΔS = }-\text{nRln}\frac{{\text{P}}_{\text{2}}}{{\text{P}}_{\text{1}}}{\text{ + nC}}_{\text{p}}\text{ln}\frac{{\text{T}}_{\text{2}}}{{\text{T}}_{\text{1}}}\text{ -----(4)}$