---
title: "Chamber with two compartments: absolute pressures, gauge C"
subject: "Fundamental of Thermodynamics & Heat Transfer"
chapter: 1
key: "semester_2/fundamental_of_thermodynamics_and_heat_transfer:large-chamber-gauges-a300-b120"
source: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/large-chamber-gauges-a300-b120
site: BCT Engineering
---

# Chamber with two compartments: absolute pressures, gauge C

Fundamental of Thermodynamics & Heat Transfer · Chapter 1: Introduction

- Asked in: 2068 Magh, 6 marks
- Video: [Pressure | Thermodynamics | (Solved examples)](https://www.youtube.com/watch?v=VSBiVsLuK8c) — Question Solutions
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/large-chamber-gauges-a300-b120
- Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-1

## Question

A large chamber is separated into compartments 1 and 2, as shown in Figure P.8, which are kept at different pressure. Pressure gauge A reads 300 kPa and pressure gauge B reads 120 kPa. If the local barometer reads 720 mm Hg, determine the absolute pressure existing in the compartments and the reading of gauge C. Take ρ = 13600 kg/m³ and g = 9.81 m/s².
[Figure P.8: a chamber with compartments 1 and 2 in a row; gauge A on the left end (compartment 1), gauge B on the partition between 1 and 2, gauge C on the right end (compartment 2).]

## Short answer

Absolute pressures: compartment 1 = 396.06 kPa, compartment 2 = 276.06 kPa. Gauge C reads 180 kPa. Atmospheric pressure is 96.06 kPa.

## Answer

**Given:** P_A = 300 kPa, P_B = 120 kPa, barometer = 720 mm Hg, ρ = 13600 kg/m³, g = 9.81 m/s².

**Assumption:** Gauge A reads compartment 1 above atmosphere, gauge B reads P₁ − P₂ across the partition, gauge C reads compartment 2 above atmosphere.

**Step 1: Atmospheric pressure**
P_atm = 13600 × 9.81 × 0.720 = 96 060 Pa = 96.06 kPa

**Step 2: Compartment 1**
P₁ = P_atm + P_A = 96.06 + 300 = **396.06 kPa (abs)**

**Step 3: Compartment 2**
P₂ = P₁ − P_B = 396.06 − 120 = **276.06 kPa (abs)**

**Step 4: Gauge C**
P_C = P₂ − P_atm = 276.06 − 96.06 = **180 kPa**

**Answer: P₁ = 396.06 kPa, P₂ = 276.06 kPa (abs); gauge C reads 180 kPa.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. A 720 mm Hg barometer with rho = 13600 gives P_atm of about
   A. 72.0 kPa
   B. 101.3 kPa
   C. 96.06 kPa
   D. 720 kPa
   Answer: C. 13600 x 9.81 x 0.72 = 96 060 Pa. (Key point: Atmospheric pressure)

2. Absolute pressure in compartment 1 is
   A. 300 kPa
   B. 204 kPa
   C. 180 kPa
   D. 396.06 kPa
   Answer: D. P1 = P_atm + P_A = 96.06 + 300 = 396.06 kPa. (Key point: Compartment 1)

3. Gauge B reads P1 - P2 = 120 kPa. P2 absolute is
   A. 276.06 kPa
   B. 516.06 kPa
   C. 120 kPa
   D. 180 kPa
   Answer: A. P2 = 396.06 - 120 = 276.06 kPa. (Key point: Compartment 2)

4. Gauge C reads
   A. 276.06 kPa
   B. 180 kPa
   C. 96.06 kPa
   D. 120 kPa
   Answer: B. P_C = P2 - P_atm = 276.06 - 96.06 = 180 kPa. (Key point: Gauge C)

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