Chapter 3, Problem 3.28P

(a)

Interpretation Introduction

Interpretation:

To find the values of $Q$, $W$, $\Delta U$ and $\Delta H$ for each step in a cyclic process occur in closed system. The cyclic process consists a ideal gas initially at ${\text{30}}^{\text{o}}\text{C}$ and $\text{100}\text{KPa}$ compressed adiabatically to pressure $\text{500}\text{KPa}$ then cooled at constant pressure of $\text{500}\text{KPa}$ to temperature ${\text{30}}^{\text{o}}\text{C}$ and finally expanded to its original state.

Concept Introduction:

In order to find all the properties of cyclic process we must find out properties of individual steps.

For adiabatic compression from point 1 to point 2, the following formulas are applicable:

  $Q{}_2=0$ since there is no heat transfer in adiabatic process.

  $T_2=T_1{(\frac{P_2}{P_1})}^{\raisebox{1ex}{$\gamma -1$}\!\left/ \!\raisebox{-1ex}{$\gamma $}\right.}$

  $\Delta U_{12}=C_V(T_2-T_1)$

  $\Delta H_{12}=C_P(T_2-T_1)$

  $W_{12}=\Delta U_{12}$

For cooling at constant pressure from point 2 to point 3, the following formulas are applicable:

  $\Delta U_{23}=C_V(T_3-T_2)$

  $W_{23}=\Delta U_{23}-Q{}_3$

  $\Delta H_{23}=Q{}_3$

  $\Delta H_{23}=C_P(T_3-T_2)$

For isothermal expansion from point 3 to point 1, the following formulas are applicable:

  $\Delta U_{31}=\Delta H_{31}=0$

  $W_{31}=R{T}_3\ln (\frac{P_1}{P_3})$

  $Q{}_1=-W_1$

(b)

Interpretation Introduction

Interpretation:

To find the values of $Q$, $W$, $\Delta U$ and $\Delta H$ for each step in a cyclic irreversible process with an efficiency $\text{80\%}$ occur in closed system. The cyclic process consists a ideal gas initially at ${\text{30}}^{\text{o}}\text{C}$ and $\text{100}\text{KPa}$ compressed to pressure $\text{500}\text{KPa}$ then cooled at constant pressure of $\text{500}\text{KPa}$ to temperature ${\text{30}}^{\text{o}}\text{C}$ and finally expanded to its original state.

Concept Introduction:

In order to find all the properties of cyclic process we know that each step has $\text{80\%}$ efficiency. So, all the properties will be same except $Q$ and $W$ .