Chapter 4.4, Problem 29P

Liquid HFC-134a at its boiling point at 12 bars pressure is throttled to 1 bar pressure. What is the final temperature? What fraction of liquid vaporizes?

To determine

The final temperature and the fraction of liquid that vaporizes.

Answer to Problem 29P

  $-26.4°\text{C}$ ; 0.465

Explanation of Solution

Given:

Initial pressure, P =12 bars

Final pressure, P = 1 bar

Formula used:

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

Here, a is the fraction of the HFC-134a, which ends up as liquid.

Calculation:

Initial temperature and enthalpy of the HFC-134a at the pressure of 12.0 bar using table 4.3 is as follows:

  $T_i=46.3\text{°C}$

  $H_i=116\text{kJ}$

The final temperature HFC-134a at the pressure of 12.0 bar is as follows:

  $Tf=-26.4°\text{C}$

  $=\left(-26.4+273\right)\text{K}$

  $=246.\text{6}\text{K}$

Hence, the final temperature of the liquid HFC-134a is $-26.4°\text{C}$ or $246.6\text{K}$

At the boiling point, the enthalpy of the liquid phase of HFC-134a at the final pressure of 1.0bar is 16 kJ while thatof the gas phase would be 231 kJ.

  $H_{liquid}=16\text{kJ}$

  $H_{\text{gas}}=231\text{kJ}$

The enthalpy is conserved to a throttling process. The initial enthalpy of the liquid HFC-134a116 kJlies between 16 kJ and 231 kJ.The final state of the HFC-134a is a combination of liquid and gas at the boiling point $-26.4°\text{C}$

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

Substitute $16\text{kJ}$ for $H_{liquid}$

  $231\text{kJ}$ for $H_{gas}$

  $H_f=a\left(16\text{kJ}\right)+\left(1-a\right)\left(231\text{kJ}\right)$

  $=231\text{kJ}-\left(215\text{kJ}\right)a$

The initial and final enthalpies of HFC-134a are equal to each other.

  $H_f=H_i$

Substitute $231\text{kJ}-\left(215\text{kJ}\right)a$ for $H_f$ and $116\text{kJ}$ for $H_i$

  $\text{231}\text{kJ-}\left(\text{215}\text{kJ}\right)\text{a}\text{=116}\text{kJ}$

Solve the equation for a

  $a=\frac{\text{231}\text{kJ-116 kJ}}{\text{215 kJ}}$

  $=0.535$

Hence, the fraction of liquid vaporizes is as follows:

  $1-a=1-0.535$

  $=0.465$

Therefore, thefraction of the liquid vaporizes is0.465.

Conclusion:

Thus, the liquid vaporization is $0.465$ .