Dimensional Consistency
The equation of state for a real gas is (P + a/V²)(V - b) = RT, where a and b are constants. The dimensions of 'a' are:
Select the correct option:
🔒 Solution Hidden from View
Submit your answer to unlock the detailed step-by-step solution.
More units and measurements Practice Questions
Considering v as velocity, v_0 as initial velocity, a as acceleration, t as time and x as distance, ...
Considering v as velocity, v_0 as initial velocity, a as acceleration, t as time and x as distance, ...
The distance between the Sun and Earth is approximately 1.5 × 10¹± m. What is its order of magnitude...
The distance between the Sun and Earth is approximately 1.5 × 10¹± m. What is its order of magnitude...
The value of the universal gas constant R depends upon:
The value of the universal gas constant R depends upon:
Using dimensional analysis, determine which of the following cannot be the formula for the time peri...
Using dimensional analysis, determine which of the following cannot be the formula for the time peri...
A screw gauge has 50 divisions on its circular scale and moves forward by 0.5 mm when the circular s...
A screw gauge has 50 divisions on its circular scale and moves forward by 0.5 mm when the circular s...
Which of the following physical quantities does NOT have the dimensional formula [M⁰L⁰T⁻¹]?
Which of the following physical quantities does NOT have the dimensional formula [M⁰L⁰T⁻¹]?
If energy (E), velocity (v), and force (F) are taken as fundamental quantities, what is the dimensio...
If energy (E), velocity (v), and force (F) are taken as fundamental quantities, what is the dimensio...
The parallax of a celestial object is 0.5 arc seconds. What is the distance to this object in parsec...
The parallax of a celestial object is 0.5 arc seconds. What is the distance to this object in parsec...
The period of oscillation of a simple pendulum is T = 2π√(L/g). If the error in measurement of L is ...
The period of oscillation of a simple pendulum is T = 2π√(L/g). If the error in measurement of L is ...
Five measurements of a length give the values 5.03 m, 5.08 m, 5.05 m, 5.07 m, and 5.02 m. What is th...
Five measurements of a length give the values 5.03 m, 5.08 m, 5.05 m, 5.07 m, and 5.02 m. What is th...
The dimension of the quantity (1/2)ε₀E² (where ε₀ is the permittivity of free space and E is the ele...
The dimension of the quantity (1/2)ε₀E² (where ε₀ is the permittivity of free space and E is the ele...
The resistance R = V/I where V = (100 ± 5) V and I = (10 ± 0.2) A. What is the percentage error in R...
The resistance R = V/I where V = (100 ± 5) V and I = (10 ± 0.2) A. What is the percentage error in R...
About This Question
- Subject
- physics
- Chapter
- units and measurements
- Topic
- dimensional consistency
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
[ML⁵T⁻²]
- Principle of Homogeneity: Only physical quantities with identical dimensions can be added or subtracted.
- Analysis of Term (P+a/V2):
- Dimension of a/V2 must equal dimensions of Pressure P.
- Derive 'a' Dimensions:
- [a]=[P]×[V2].
- Dimensions of P (Pressure): Force/Area =[ML−1T−2].
- Dimensions of V2 (Volume squared): ([L3])2=[L6].
- Calculation:
- [a]=[ML−1T−2]×[L6]=[ML5T−2].
- Result: The dimensions of the Van der Waals constant 'a' are [ML5T−2].
This medium difficulty physics question is from the chapter units and measurements, covering the topic of dimensional consistency. It appeared in the 2025 exam.
Looking for more practice? Explore all physics questions or browse units and measurements questions on RankGuru.