Pressure measurement – meaning of vacuum pressure Is it correct to say that “vacuum pressure” is always the negative of the gauge pressure (i.e., vacuum pressure = − gauge pressure when pressure is below atmospheric)?

Introduction:
Different reference frames for pressure—absolute, gauge, and vacuum—can be confusing. This question checks the algebraic relationship between gauge pressure and vacuum pressure when a system is below atmospheric pressure.

Given Data / Assumptions:

• Atmospheric pressure p_atm is the local reference.
• Gauge pressure p_g = p_abs − p_atm.
• Vacuum pressure p_vac is the shortfall below atmospheric: p_vac = p_atm − p_abs when p_abs < p_atm.

Concept / Approach:
Combining the definitions gives p_vac = − p_g for sub-atmospheric conditions. Thus, a gauge reading of −30 kPa corresponds to a vacuum pressure of +30 kPa (of vacuum), while absolute pressure is p_abs = p_atm − 30 kPa.

Step-by-Step Solution:
1) Write gauge: p_g = p_abs − p_atm.2) Write vacuum: p_vac = p_atm − p_abs.3) Therefore p_vac = −(p_abs − p_atm) = −p_g.4) Hence the statement is correct as a definition for sub-atmospheric systems.

Verification / Alternative check:
Manometer readings referenced to atmosphere invert when switching from gauge to vacuum scale, consistent with p_vac = −p_g.

Why Other Options Are Wrong:

• No: contradicts the algebraic relation.
• Only for ideal gases / only when temperature is constant: the relation is definitional and independent of equation of state or temperature.

Common Pitfalls:
Mixing absolute and gauge numbers; reporting “−30 kPa vacuum” (nonsensical)—vacuum is reported as a positive shortfall, while gauge may be negative.

Final Answer:
Yes