# Understanding specific volume(introductory thermodynamics)

1. Dec 11, 2013

### wahaj

Specific volume is the volume occupied by 1 kg of a material. This part is simple to understand. Say I have some fluid at a temperature and pressure. I can find the specific volume for it by looking at the tables and find its quality. Simple enough. Now lets move to stage two where one or all properties (temperature, pressure and volume) change. Now I must find the quality again. At this point why do I keep the same specific volume as in the previous stage (vf & vg change of course). I mean if you decrease the pressure you would expect each kg of gas to occupy more space which would change the specific volume found initially.
Propane is contained in a rigid container at 8 bar and 80°C. Propane is in the vapor region under these conditions . If pressure drops to 5 bar find the quality. At 5 bar propane is in the liquid-vapor region. My question again is that why do we use the specific volume found at 8 bar and 80°c to find the quality at 5 bar and some new temperature.

2. May 4, 2015

### jlefevre76

When it comes to finding quality, usually you need a phase change properties table to reference the values needed to find the quality. Quality is defined as:

$$x=\frac{v-v_f}{v_g-v_f}=\frac{u-u_f}{u_g-u_f}=\frac{h-h_f}{h_g-h_f}=\frac{s-s_f}{s_g-s_f}$$

So, really in the phase change region, you need one of these tables to get the desired values. If your thermodynamics textbook doesn't have propane, try googling saturated propane table, including temperature if you know the temperature, or pressure if you know the pressure.

As for specific volume, for liquids it's dependent on temperature. For gases:
Specific volume: $$v=\frac{RT}{P}$$
Density: $$\rho=\frac{P}{RT}$$
For gases or liquids: $$\rho=\frac{1}{v}$$
$$v=\frac{1}{\rho}$$

Last edited: May 4, 2015
3. May 4, 2015

### Randy Beikmann

In the problem you posed, the container is rigid, so the volume cannot change. Since no material is leaving or entering the container, the mass is also constant. All of which means the specific volume is constant. The pressure and temperature have changed, but not the volume.
Of course this isn't always true. It was just a "given" for this problem.

4. May 4, 2015

### Staff: Mentor

To add to what Randy said, in the case where some propane has condensed out, the specific volume they are referring to is the average specific volume (i.e., the mass weighted average of the specific volumes of the liquid and vapor). This average specific volume doesn't change, because the mass of material in the container and the volume of the container has not changed.

Chet