Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
186 views
in General by (115k points)
closed by
A reservoir of capacity 0.01 m3 is completely filled with a fluid of coefficient of compressibility 0.75 × 10-9 m2/N. The amount of fluid that will spill over (in m3), if pressure in the reservoir is reduced by 2 × 107 N/m2 is
1. 1 × 10-4
2. 1.5 × 10-4
3. 0.15 × 10-4
4. None of the above

1 Answer

0 votes
by (152k points)
selected by
 
Best answer
Correct Answer - Option 2 : 1.5 × 10-4

Concept:

In thermodynamics and Fluid Engineering, compressibility is a measure of the relative volume change of a fluid as a response to pressure (or mean stress) change.

Compressibility in Fluid Engineering is expressed as follows:

\(β=\frac{1}{K} = \frac{{ - 1}}{{\frac{{VdP}}{{dV}}}} = -\frac{{dV}}{{VdP}}\)

where, ∂p = change of pressure, ∂v = change in the volume

K = bulk modulus

(-ve) sign indicates, there is a decrease in volume due to an increase in pressure.

Calculation:

Given:

β = 0.75× 10-9 m2/N, V = 0.01 m3, dP = 2× 107 Pa

Compressibility (β) = \(\frac{1}{k} = \frac{{ - 1}}{{\frac{{VdP}}{{dV}}}} = \frac{{ - dV}}{{VdP}}\)

\(\left( β \right) = \frac{{ - dV}}{{VdP}}\)

\(0.75 × {10^{ - 9}} = - \frac{{ - dV}}{{0.01 × \left( { - 2 × {{10}^7}} \right)}}\)

dV = 1.5 × 10-4

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...