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