Unit conversion check: 1 Pascal (Pa), the SI unit of pressure, equals how many newtons per square metre (N/m^2)?
Chemical Engineering
Stoichiometry
Difficulty: Easy
Choose an option
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A10
-
B1
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C0.1
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D1000
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E0.01
Answer
Correct Answer: 1
Explanation
Introduction / Context:Consistent SI unit handling prevents serious design and safety errors. Pressure appears in fluid mechanics, thermodynamics, and transport operations; the Pascal is the SI coherent unit.
Given Data / Assumptions:
- Definition of Pascal: 1 Pa = 1 N acting uniformly over 1 m^2.
- Derived from base SI units: kg, m, s.
Concept / Approach:By definition, pressure = force / area. The SI unit of force is the newton (N), and area is in square metres (m^2). Hence, 1 Pa = 1 N / m^2 exactly. Larger units include kPa (10^3 Pa) and MPa (10^6 Pa).
Step-by-Step Solution:
Write formula: P = F / A.Insert units: Pa = N / m^2.Conclude 1 Pa equals 1 N per m^2 by definition.Recognize scaling: 1 kPa = 1000 N/m^2.Verification / Alternative check:Dimensional analysis from base units shows Pa = kg·m^−1·s^−2, matching N/m^2.
Why Other Options Are Wrong:
- 10, 0.1, 1000, 0.01 N/m^2: incorrect scaling; these correspond to deca-, deci-, kilo-, centi- multiples not aligned with the base definition.
Common Pitfalls:Confusing Pa with bar: 1 bar = 10^5 Pa = 100 kPa.
Final Answer:1