Question

Two kg of a two phase liquid vapor mixture of carbon dioxide(co2) exists at a - 40C in a 0.05 tank

Answer 1

The question is incomplete. Here is the complete question.

Two kg of a two phase liquid vapor mixture of carbon dioxide (CO₂) exists at -40°C in a 0.05m³ tank. Determine the quality of the mixture, if the values of specific volume for saturated liquid and saturated vapor CO₂ at -40°C are $v_{f}$ = 0.896 x 10⁻³m³/kg and $v_{g}=$ 3.824 x 10⁻²m³/kg, respectively.

Answer: x = 1

Explanation: In a phase change of a pure substance, at determined pressure and temperature, the substance exists in two different phases: saturated liquid and saturated vapor.

Quality (x) is the ratio of saturated vapor in the mixture and can be written as:

$x=\frac{m_{vapor}}{m_{liquid}+m_{vapor}}$

It has value between 0 and 1: x = 0 for saturated liquid and x = 1 for saturated vapor.

When related with volumes, quality is rearranged as:

$x=\frac{v-v_{f}}{v_{g}-v_{f}}$

Solving for x:

$x=\frac{0.05-0.896.10^{-3}}{3.824.10^{-2}-0.896.10^{-3}}$

$x=\frac{0.049104}{0.037344}$

x = 1.3

Quality of mixture of carbon dioxide is x = 1, which means it's for saturated vapor.