If the gauge pressure and atmospheric pressure at a point are observed as 70 mm of mercury and 750 mm of mercury respectively. What is the value of the absolute pressure (mm of mercury) at that point?

Asked in SSC JE 29-01-2018 (Evening Shift)

Detailed Explanation

Absolute pressure represents the total pressure measured relative to absolute zero pressure (complete vacuum). For any system at positive gauge pressure, absolute pressure is the sum of local atmospheric and gauge pressure.

1. State the given pressure values in consistent units (\(\text{mm of Hg}\)):

• Atmospheric pressure \(p_{\text{atm}} = 750\text{ mm of Hg}\)
• Gauge pressure \(p_{\text{gauge}} = 70\text{ mm of Hg}\)

2. Apply the fundamental pressure equation:

\[ p_{\text{abs}} = p_{\text{atm}} + p_{\text{gauge}} \]

3. Substitute the values:

\[ p_{\text{abs}} = 750\text{ mm of Hg} + 70\text{ mm of Hg} = 820\text{ mm of Hg} \]

Why “820” Is Correct

Adding the excess gauge pressure of \(70\text{ mm of Hg}\) above atmospheric pressure to the ambient atmospheric level of \(750\text{ mm of Hg}\) gives an absolute pressure of \(820\text{ mm of Hg}\).

Why the Other Options Are Wrong

• A. 500: 500 mm Hg is an arbitrary number with no connection to the given data.
• B. 680: 680 mm Hg results from mistakenly subtracting gauge pressure: 750 − 70 = 680 mm Hg (which would give absolute pressure for a vacuum).
• C. 750: 750 mm Hg is simply the atmospheric pressure alone, ignoring the positive gauge pressure.

Key Concepts for Students

• When gauge pressure is positive, absolute pressure is always greater than atmospheric pressure.
• When gauge pressure is negative (vacuum), absolute pressure is less than atmospheric: p_abs = p_atm − p_vac.
• Pressure heads of the same fluid can be directly added or subtracted.

Practice more: this is question 16 in Measurement of Pressure MCQs – Part 2. Try the whole set and check every answer instantly.