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 properties and behavior of a superheated vapour step-by-step:

1. Definition of Superheated Vapour:
A superheated vapour is a state of a substance where its temperature is higher than its saturation temperature (boiling point) at a given pressure. In this state, the vapour is completely dry and behaves similarly to a gas, meaning that any cooling will not immediately cause condensation unless the temperature drops to the saturation temperature.

2. Comparing Pressures at a Given Temperature:
Let us consider a fixed temperature,
$T$
If we look at a typical pressure-temperature (P-T) or pressure-volume (P-v) diagram, for a given temperature, the phase changes from liquid to vapour at the saturation pressure,
$P_{\text{sat}}$
If the actual pressure
$P$
is reduced below this saturation pressure (i.e.,
$P<P_{\text{sat}}$
), the molecules are further apart, and the substance enters the superheated vapour region. Therefore, at a given temperature, a superheated vapour always exists at a pressure less than the saturation pressure.

3. Why the other options are incorrect:
• Its temperature is less than the saturation temperature at a given pressure: Incorrect, because by definition, a superheated vapour must have a temperature higher than the saturation temperature (
$T>T_{\text{sat}}$
) at a given pressure. If it were less, it would be a compressed liquid or subcooled liquid.
• Its volume is less than the volume of the saturated vapour at a given temperature: Incorrect, because as pressure decreases at a constant temperature, the specific volume of the gas increases (following the ideal gas relationship
$v\propto 1/P$
). Thus, the volume of superheated vapour is greater than that of saturated vapour at the same temperature.
• Its enthalpy is less than the enthalpy of the saturated vapour at a given pressure: Incorrect, because heating a saturated vapour to become superheated requires the addition of sensible heat, which increases its enthalpy. Thus, superheated vapour has a higher enthalpy than saturated vapour at the same pressure.