For a liquid/vapor system in equilibrium at ps and To, if the pressure po is lower than the saturation
pressure corresponding to the system temperature 7a, the system is
a) compressed liquid
b) superheated vapor
c) a mixture of liquid & vapor
d) undetermined
The correct answer and explanation is :
The correct answer is b) superheated vapor.
Explanation:
In thermodynamics, the state of a substance in a liquid-vapor system depends on its pressure and temperature. When a substance is in equilibrium between its liquid and vapor phases, it exists as a saturated mixture. The system is at a saturation condition when the pressure of the substance is equal to the saturation pressure at the given temperature.
The saturation pressure, (p_{sat}), is the pressure at which a substance changes between its liquid and vapor phases at a specific temperature (T_0). When a substance is at saturation pressure, it exists as a saturated mixture of liquid and vapor, with some amount of liquid and some amount of vapor present in equilibrium.
However, in this case, we are told that the actual pressure (p_0) is lower than the saturation pressure corresponding to the system temperature (T_0). This condition means that the pressure is insufficient to support the vapor phase at that temperature. To understand what happens, we must look at the behavior of substances under different pressure and temperature conditions.
- If the pressure is lower than the saturation pressure for a given temperature, it means that the substance cannot exist as a mixture of liquid and vapor at that temperature.
- At lower pressures, the substance cannot remain in the saturated state, and the vapor phase will expand beyond the point of saturation, causing it to become superheated.
- A superheated vapor is a vapor that is not in equilibrium with liquid at a given temperature and pressure. The substance exists entirely as a vapor, and its temperature is higher than the boiling point for the corresponding pressure.
Thus, when the pressure (p_0) is lower than the saturation pressure (p_{sat}), the substance must be in the superheated vapor state. Therefore, the correct answer is b) superheated vapor.