Dew point behavior — For a fixed gas–vapor composition, how does the dew point temperature change with system pressure?

Introduction:Dew point is the temperature at which a gas–vapor mixture becomes saturated upon cooling at fixed total pressure and composition. Understanding how dew point varies with pressure is important for condensers, dryers, and compressed air systems.

Given Data / Assumptions:

• Gas–vapor mixture with fixed vapor mole fraction (composition constant).
• Total pressure is varied.
• Equilibrium governed by vapor–liquid equilibrium and saturation properties.

Concept / Approach:At dew point, the saturation pressure of the vapor at the dew-point temperature equals its partial pressure in the mixture: p_sat(T_dew) = y_v * P_total. Holding y_v constant, increasing P_total raises the vapor partial pressure at the dew point. Since p_sat(T) increases monotonically with T, a higher p_sat requirement implies a higher dew-point temperature. Conversely, lowering total pressure lowers dew point.

Step-by-Step Solution:Write the dew-point condition: p_sat(T_dew) = y_v * P.Increase P → required p_sat increases.Because p_sat grows with T, T_dew must increase.

Verification / Alternative check:Compressed air dryers experience condensation at warmer surfaces after compression because the dew point rises with pressure—operational evidence of this relationship.

Why Other Options Are Wrong:

• (a) and (b) conflate dew point (a function of pressure and composition) with dry-bulb temperature changes.
• (c) True statement but opposite direction to (d); only one should be selected—(d) is the direct phrasing.
• (e) Dew point is not pressure independent.

Common Pitfalls:Assuming dew point is a property of composition alone; ignoring the role of total pressure.

Final Answer:It increases with an increase in total pressure