91Ó°ÊÓ

The final temperature and the fraction of liquid that vaporizes

Given:

Initial pressure, P=12 bars

Final pressure, P=1 bar

Formula: $H_f=a\left(H_{\text{liquid}}\right)+(1-a)\left(H_{gas}\right)$

$\text{Where,}a=\text{is the fraction of the HFC-134a, which ends up as liquid.}$

Calculation:

Using table 4.3, the initial temperature and enthalpy of the HFC $-134a$at a pressure of 12.0 bar are as follows:

$$\begin{gathered} T_i=46.3°\mathrm{C} \\ {\mathrm{H}}_{\mathrm{i}}=116\mathrm{kJ} \end{gathered}$$

At a pressure of 12.0 bar, the final temperature of HFC-134a is as follows:

$$\begin{gathered} Tf=-26.4°\mathrm{C} \\ =(-26.4+273)\mathrm{K} \\ =246.6\mathrm{K} \end{gathered}$$

$$\begin{gathered} \text{Therefore, the final temperature of the liquid}\mathrm{HFC}-134\mathrm{a}\text{is} \\ -26.4°\mathrm{C}\text{or}246.6\mathrm{K} \end{gathered}$$

The enthalpy of the liquid phase of HFC-134a at the boiling point at a final pressure of 1.0 bar is $16\mathrm{kJ}$, while the gas phase is$231\mathrm{kJ}$.

$$\begin{gathered} H_{\text{liquid}}=16\mathrm{kJ} \\ {\mathrm{H}}_{\mathrm{gas}}=231\mathrm{kJ} \end{gathered}$$

A throttling operation conserves the enthalpy. The initial enthalpy of liquid HFC-134a ranges from$16\mathrm{kJ}$to $231\mathrm{kJ}$. The boiling point of

HFC-134a is $-26.4°\mathrm{C}$, which results in a mixture of liquid and gas.

$H_f=a\left(H_{\text{liquid}}\right)+(1-a)\left(H_{gas}\right)$

Substitute$H_{\text{liquid}}=$$16\mathrm{kJ}$

$H_{gas}=$$231\mathrm{kJ}$

$$\begin{gathered} H_f=a(16\mathrm{kJ})+(1-a)(231\mathrm{kJ}) \\ =231\mathrm{kJ}-(215\mathrm{kJ})a \end{gathered}$$

HFC-134a has the same initial and ultimate enthalpies as water.

$H_f=H_i$

$$\begin{gathered} \text{Substitute}{H}_f=231\mathrm{kJ}-(215\mathrm{kJ})a \\ {H}_i=116\mathrm{kJ} \end{gathered}$$

solving for a is :

$$\begin{gathered} a=\frac{231\mathrm{kJ}-116\mathrm{kJ}}{215\mathrm{kJ}} \\ =0.535 \end{gathered}$$

Hence, the fraction of liquid vaporizes is as follows:

role="math" localid="1648690588799" $$\begin{gathered} 1-a \\ =1-0.535 \\ =0.465 \end{gathered}$$

Thus, the liquid vaporization is 0.465 .