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Three gauges: absolute pressure in compartment 2, gauge c

Short answer

Compartment 2 absolute pressure is 0.6 MPa, gauge C reads 0.5 MPa. With P_atm=0.1 MPa, P₁=1.1 MPa abs, P₂=1.1-0.5=0.6 MPa abs, gauge C=0.6-0.1=0.5 MPa.

Attached to the containers shown in figure below are three pressure gauges. Determine the absolute pressure in compartment 2 and reading of pressure gauge c. [Figure: two compartments 1 and 2 side by side; gauge a on top of compartment 1 reads Pa = 1.0 MPa; Patm = 1.0 MPa (as printed); gauge b on the partition reads Pb = 0.5 MPa; gauge c on compartment 2.]

Given: P_a = 1.0 MPa (gauge on compartment 1), P_b = 0.5 MPa (gauge on the partition, reads the difference P₁ − P₂), gauge c on compartment 2.

Note on P_atm: The data print P_atm = 1.0 MPa, which is evidently a misprint for 0.1 MPa (about 1 atm). The solution uses P_atm = 0.1 MPa.

Step 1: Compartment 1 P₁ = P_atm + P_a = 0.1 + 1.0 = 1.1 MPa (abs)

Step 2: Compartment 2 P₂ = P₁ − P_b = 1.1 − 0.5 = 0.6 MPa (abs)

Step 3: Gauge c P_c = P₂ − P_atm = 0.6 − 0.1 = 0.5 MPa

Answer: Absolute pressure in compartment 2 = 0.6 MPa; gauge c reads 0.5 MPa.

The gauge-c reading, 0.5 MPa, equals P_a − P_b and does not depend on the value of P_atm. (If the printed P_atm = 1.0 MPa were used, the absolute pressure would be 1.5 MPa and gauge c would still read 0.5 MPa.)

✓ Answer checked by Claude Opus 5.5 (high effort)

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