Physics Thermodynamics UHS 2023
PMDC Verified Question 16 of 54
For an ideal gas equation \(PV = nRT\), the dimensions of real gas constant R are:
A
\([M L^{-2} T^{-1} K^{-1}]\)
B
\([M L^2 T^{-2} K^{-1}]\)
C
\([M L^{-3} T^{-2} K^{-1}]\)
D
\([M L^{-3} T^{-1} K^{-1}]\)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: \([M L^2 T^{-2} K^{-1}]\)
1. Concept:

Dimensional analysis is used to find the base SI units of a constant by isolating it in a known physical equation.

2. Formula:

$$R = \frac{PV}{nT}$$

3. Solution:

  • The product of Pressure and Volume (\(PV\)) has the exact same dimensions as Energy or Work (Joules).


  • The dimension of Energy is \([M L^2 T^{-2}]\).


  • Temperature (\(T\)) has the dimension of \([K]\). Moles (\(n\)) are dimensionless or defined as \([mol]\), but often omitted in basic dimensional brackets.


  • Dividing Energy by Temperature yields: \([M L^2 T^{-2} K^{-1}]\).


4. Why other options are incorrect:

Other dimensional formulas represent incorrect physics, such as dividing by volume instead of multiplying (yielding negative length dimensions).

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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