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Grade -11 (NEB) > Science Physics Dimensional Analysis and Applications, Physical Quantities

Check the correctness of the formula, PV = RT using dimensional method.

Check the correctness of the formula, PV = RT using the dimensional method.

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Solution:

Given formula: PV = RT, where, P = pressure,

V = volume, R = gas constant and T = temperature.

The dimension of pressure, P = [M L-1 T-2]

The dimension of volume, V = [L3]

The dimension of gas constant, R = [M L2 T-2 K-1]

The dimension of temperature, T = [K]

Now,

Dimension of left hand side, PV = [M L-1 T-2 L3] = [M L2 T-2]

Dimension of right hand side, RT = [M L2 T-2 K-1 K] = [M L2 T-2]

Since the dimensions on the right-hand side are equal to the dimensions on the left-hand side of a formula PV = RT.

Hence, the formula is dimensionally correct.

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Things to Remember From Physical Quantities

  • The four applications of dimensional analysis are:
    • To check the correctness of physical relation.
    • To derive the relation between various physical quantities.
    • To convert the value of physical quantities from one system of units into another system of units.
    • To find the dimensions of constants in the given equation.

  • The correctness of physical relation can be determined by comparing the dimension of the left-hand side (LHS) and the dimension of the right-hand side (RHS)
  • We can use the formula, \(N_2=N_1\left[\frac{M_1}{M_2}\right]^a\left[\frac{L_1}{L_2}\right]^b\left[\frac{T_1}{T_2}\right]^c\)\) to convert unit from one to another system using dimension.

  • Despite the usefulness of dimensions, there are some limitations. They are:
    • The dimensional analysis does not give any information about dimensionless constants.
    • If the quantity depends on more than three other physical quantities having dimensions, the formula cannot be derived.
    • We cannot derive the formula containing trigonometric functions, logarithmic functions, exponential functions, etc. It is best suited for linear functions only.
    • The exact form of a relationship cannot be determined when there is more than one part in any relationship.
    • It gives no information about the physical quantity,

 

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