Chapter 3, Problem 3.34P

Interpretation Introduction

Interpretation:

The values of Q, W, ΔU and ΔH should be deduced for 1 mole of an ideal gas at $25\text{C}$ and 10 bar which first expands adiabatically and then heated at constant volume to a final state at $25\text{C}$ and 1 bar

Concept Introduction:

• Isothermal process proceeds with no change in temperature i.e. ΔT = 0
• Isobaric process proceeds with no change in pressure i.e. ΔP = 0
• Isochoric process proceeds with no change in volume i.e. ΔV = 0
• Isobaric process with no exchange of heat i.e. Q = 0
• Based on the first law of thermodynamics

$\begin{array}{l}\text{ΔU = Q + W ------(1)}\\ \text{where:}\\ \Delta \text{U = change in internal energy}\\ \text{Q = heat involved}\\ \text{W = work done}\end{array}$

• For an isochoric process

$\begin{array}{l}\Delta {\text{U = C}}_{\text{v}}\Delta \text{T ------(2)}\\ \text{where:}\\ \Delta \text{T = change in temperature}\\ {\text{C}}_{\text{v}}\text{ = specific heat capacity at constant volume}\end{array}$

• For an isobaric process:

$\begin{array}{l}\Delta {\text{H = C}}_{\text{p}}\Delta \text{T ------(3)}\\ \text{where:}\\ \Delta \text{H = change in temperature}\\ {\text{C}}_{\text{p}}\text{ = specific heat capacity at constant pressure}\end{array}$

• $\begin{array}{l}\text{The ratio of specific heats is given as:}\\ \text{γ = }\frac{{\text{C}}_{\text{p}}}{{\text{C}}_{\text{v}}}\text{ ---------(4)}\end{array}$