Psychrometrics — definition check: Relative humidity (often denoted by φ or RH) is defined using partial pressures. Given pv = partial pressure of water vapour, pd = saturation pressure at the dry-bulb temperature, pb = barometric pressure, ps = pressure of saturated air, pw = saturation pressure corresponding to the wet-bulb temperature, and μ = degree of saturation, choose the correct expression for relative humidity.

Introduction / Context:
Relative humidity is a core concept in HVAC and meteorology. It compares the actual moisture present in air to the maximum possible moisture the air could hold at the same temperature. Using the correct pressure terms avoids large errors in coil sizing, comfort prediction, and psychrometric chart work.

Given Data / Assumptions:

• pv = partial pressure of water vapour actually present in the air.
• pd = saturation pressure of water vapour at the current dry-bulb temperature.
• pb = barometric (total) pressure of the air–vapour mixture.
• ps = pressure of saturated air (contextual, but not needed for RH).
• pw = saturation pressure at the wet-bulb temperature.
• μ = degree of saturation (a different humidity measure).

Concept / Approach:
Relative humidity φ is the ratio of the current vapour partial pressure to the saturation vapour pressure at the same dry-bulb temperature. Therefore, φ = pv / pws, where pws here is denoted as pd. If φ is required in percent, multiply by 100. Values range from 0 to 1 (or 0% to 100%).

Step-by-Step Solution:

Verification / Alternative check:
On a psychrometric chart, for a given dry-bulb temperature, lines of constant φ correspond to pv proportional to pws at that temperature. Measured φ must always be ≤ 1 since pv ≤ pd.

Why Other Options Are Wrong:

φ = (pb − pv) / pb: mixes total pressure with vapour pressure; not RH.φ = pv / pw: uses saturation at wet-bulb temperature, not at dry-bulb; incorrect.φ = μ * ps / pb: degree of saturation μ is not equal to relative humidity and requires additional relations.none of these: incorrect since φ = pv / pd is valid.

Common Pitfalls:
Confusing relative humidity with humidity ratio (mass basis) or using wet-bulb saturation pressure instead of dry-bulb saturation pressure. Always pair φ with the saturation pressure at the same temperature.

Final Answer:

φ = pv / pd