# Chemical Process Calculation Questions and Answers – Dimensional Consistency

This set of Chemical Process Calculation Multiple Choice Questions & Answers (MCQs) focuses on “Dimensional Consistency”.

1-3. Volume representation of a real gas is given by the equation
V = aT + bTP + cTPn Litre
Where: a,b,c are constants and T, P, n are temperature, pressure and number of moles respectively.
If the equation is dimensionally consistent then
1. What is the unit of a?
a) L/K
b) L/(K)(atm)
c) L/(K)(atm)(mole)
d) None of the mentioned

Explanation: Unit of a = unit of V / unit of T.

2. What is the unit of b?
a) L/K
b) L/(K)(atm)
c) L/(K)(atm)(mole)
d) None of the mentioned

Explanation: Unit of b = unit of V / (unit of T)(Unit of P).

3. What is the unit of c?
a) L/K
b) L/(K)(atm)
c) L/(K)(atm)(mole)
d) None of the mentioned

Explanation: Unit of c = unit of V / (unit of T)(Unit of P)(unit of n).

4. A relation of distance with time is given as d = 25(1-exp(-0.021t)) µm where d is in microns and t in seconds. What is the relation if d is in inches and t in minutes?
a) 25(1-exp(-0.021t)) in
b) 1.64(1-exp(0.26t)) in
c) 3.84(1-exp(0.26t)) in
d) 9.84(1-exp(1.26t)) in

Explanation: Each term in an equation must have same dimensions and units as every other term to which it is added or subtracted or equated.

5. Given relation are-
A. T = 4π[l/g]0.5
Where: l- length, g- gravity, T- time period of a pendulum
B. ∆P = v2*(L/D)
Where: ∆P- Pressure drop, L- length of pipe and D- Diameter of the pipe
Having dimensional consistency
a) 1
b) 2
c) Both 1 and 2
d) Neither 1 nor 2

Explanation: Units of left hand-side of the equation match the units of the right-hand side, the equation is dimensionally consistent.

6. For dimensional consistency each term in an equation must have the same net dimension and unit as every other term to which it is added or subtracted or equated.
The above given statement is
a) False
b) True
c) Not mandatory
d) None of the mentioned

Explanation: For dimensional consistency each term in an equation must have the same net dimension and unit as every other term to which it is added or subtracted or equated.

7. A collection of variables or parameters that has no net dimensions or units are called
a) Dimensionless group
b) Dimensional group
c) Derived dimension group
d) None of the mentioned

Explanation: A collection of variables or parameters that has no net dimensions or units are called dimensionless group.

8. Find out the dimensionless quantity
a) Pressure
b) Reynolds number
c) Viscosity
d) Density

Explanation: Reynolds number has no dimension or units.

9-10. Pressure relation of a real gas is given by the equation P = Aexp(B/T) atm. Where A and B are constants and T is the temperature of the gas.

9. What is the unit of A?
a) atm
b) K
c) 1/atm
d) 1/K

Explanation: The unit of A is same as the unit of pressure.

10. What is the unit of B?
a) atm
b) K
c) 1/atm
d) 1/K

Explanation: The unit of B is same as the unit of temperature.

Sanfoundry Global Education & Learning Series – Chemical Process Calculation.
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