Question

Draw a T-v diagram of a pure substance including the liquid, vapor, and liquid/vapor region. Using this diagram, explain what happens if a saturated liquid is heated (such that the temperature rises) in a rigid (constant volume) container. Using the same diagram, explain what happens when a saturated vapor is heated (such that the temperature rises) in a rigid container.

Answer 1

Given above is a T-V of a pure substance. A pure substance can be defined as a chemical compound with fixed composition and characteristics.

As we can see in the above diagram, the T-V curve is bounded by two regions, namely the saturated liquid state (also known as the compressed liquid region) on the left and the saturated vapour state(also known as the superheated vapour region) on the right. At the critical point, the liquid and vapour phase coexist and are indistinguishable from each other.
It is essential here to understand the difference between the specific heat and latent heat of a liquid. The specific heat of any compound is the amount of heat it needs to absorb to raise its temperature by a degree for unit mass without changing its state. However, latent heat requires a change in state. At this point, the liquid will absorb heat while keeping the temperature constant to change its state.

As we consider the saturated liquid in the rigid container, it will absorb latent heat of vaporisation while keeping the temperature. As a result of this, the specific heat of the liquid increases a lot. The density of the liquid then decreases, which means that the liquid starts vaporising. The temperature remains constant until all the liquid is vaporised. Notice that midway through the phase transition process the rigid container contains half liquid and half vapour.

Since the container is rigid, the volume available for the expansion of the has remained constant. So as more and more vapour is being added to the system due to the phase change of saturated liquid, the volume of the entire system remains the same. However, we know that with the rise in temperature, a gas should expand, which is constrained in this case. Therefore, after the phase transition is complete, further heating will try to raise to the temperature of the system, but upon failing to expand it, the density will tend to decreases, the volume decreases and the vapour will start to condense. This phenomenon is also called as isobaric cooling. In this case, if the system is heated, no temperature rise can be observed but if the system is left on its own then condensing takes place, and the volume decreases