Chapter 6, Problem 6.58P

(a)

Interpretation Introduction

Interpretation:

The temperature of the expanded gas and the work produced needs to be calculated using ideal gas equations.

Concept Introduction:

For an ideal gas, the formula to calculate entropy is:

  $\frac{\Delta S}{R}=A\ln \tau +\left[B{T}_0+\left(C{T}_0^2+\frac{D}{{\tau }^2{T}_0^2}\right)\left(\frac{\tau +1}{2}\right)\right]\left(\tau -1\right)-\ln \frac{P}{P_0}$ ...... (1)

Here, $A,B,C,\text{ and }D$ are the parameters taken from table C.1 and $T_0$ is the standard temperature.

  $\tau$ is defined as:

  $\tau =\frac{T}{T_0}$

The formula to calculate the work produced by an ideal gas is:

  $W_s=\Delta H^{ig}$ ...... (2)

Here, $\Delta H^{ig}$ is defined as:

  $\Delta H^{ig}={\displaystyle {\int }_{T_1}^{T_2}{C}_p^{ig}dT}$ ...... (3)

The value of $C_p^{ig}$ is taken from table C.1.

(b)

Interpretation Introduction

Interpretation:

The temperature of the expanded gas and the work produced are to be calculated using appropriate generalized correlations.

Concept Introduction:

For a real gas, the formula to calculate entropy is:

  $\frac{\Delta S}{R}=A\ln \tau +\left[B{T}_0+\left(C{T}_0^2+\frac{D}{{\tau }^2{T}_0^2}\right)\left(\frac{\tau +1}{2}\right)\right]\left(\tau -1\right)-\ln \frac{P}{P_0}+S_2^R-S_1^R$ ...... (1)

Here, $A,B,C,\text{ and }D$ are the parameters taken from table C.1 and $T_0$ is the standard temperature.

  $\tau$ is defined as:

  $\tau =\frac{T}{T_0}$

$S_i^R$ at state $i$ is defined as:

  $S_i^R={\left(S_i^R\right)}^0+\omega {\left(S_i^R\right)}^1$ ...... (2)

Here, ${\left(S_i^R\right)}^0\text{ and }{\left(S_i^R\right)}^1$ are given in table D.9 and D.10.

The formula to calculate the work produced by a real gas is:

  $W_s=\Delta H^{ig}+H_2^R-H_1^R$ ...... (3)

Here, $\Delta H^{ig}$ is defined as:

  $\Delta H^{ig}={\displaystyle {\int }_{T_1}^{T_2}{C}_p^{ig}dT}$ ...... (4)

The value of $C_p^{ig}$ is taken from table C.1. $H_i^R$ at state $i$ is defined as:

  $H_i^R={\left(H_i^R\right)}^0+\omega {\left(H_i^R\right)}^1$ ...... (5)

Here, ${\left(H_i^R\right)}^0\text{ and }{\left(H_i^R\right)}^1$ are given in table D.5 and D.6.