Which one of the following statements is correct for a superheated vapour?

The correct option is: Its pressure is less than the saturation pressure at a given temperature.

To understand why this statement is correct, let us analyze the characteristics of a superheated vapour relative to saturated states. By definition, a superheated vapour is a vapour at a temperature higher than its vaporization (saturation) temperature at a given pressure.

Let us evaluate the relationship between pressure, temperature, and saturation states:

1. Temperature-Pressure Relationship:
For any pure substance, the saturation pressure _Psat and saturation temperature _Tsat are directly related. As temperature increases, the saturation pressure also increases.

2. Analyzing at a Given Temperature:
If we fix the temperature at a constant value, say _T, the corresponding saturation pressure is _Psat(T). For the substance to exist as a superheated vapour at this temperature _T, its actual pressure _P must be reduced below the saturation pressure. That is:
$$P<P_{\mathrm{sat}}(T)$$
This confirms that for a superheated vapour, its pressure is less than the saturation pressure at a given temperature.

3. Analyzing the other options:
- At a given pressure, a superheated vapour has a temperature greater than the saturation temperature (_{T > Tsat}). Therefore, the second option is incorrect.
- At a given temperature or pressure, superheating causes the vapour to expand, meaning its specific volume and enthalpy are greater than those of the saturated vapour (_{v > vg} and _{h > hg}). Thus, the third and fourth options are incorrect.