Question

please answer with full explanation
correct answer is*(a)*
but how???? ​

Answer 1

Answer:

a) D(a/b) = [ML^2T^-2]

Explanation:

This question can be done in two ways.

1. Find dimensions of a and b and divide
2. Simple and shortest method based on principle of homogeneity.

I'll solve this question by method 2 because getting the answer is our only target.

The given equation:

(P + a/V^2)(V - b) = RT

PV - Pb + a/V - ab/V^2 = RT

From principle of homogeneity, the dimension of each term in a dimensional equationis same.

So, D(PV) = D(Pb)

(Note D(X) means Dimension of X)

D(V) = D(b)

Consider the next term: a/V

D(a/V) = D(a)/D(V) = D(PV)

= D(a)/D(b) = D(PV)

= D(a/b) = D(P)D(V)

D(a/b) = [ML^-1T^-2][L^3]

D(a/b) = [ML^2T^-2]

Answer 2

ANSWER :

✴ Given :

$\underline{\boxed{\bf{\pink{{\huge(}P+\dfrac{a}{V^2}{\huge)}(V-b)=RT}}}}$

• P = Pressure
• V = Volume

✴ To Find :

✏ Dimensional formula of a/b

✴ Concept :

✏ Only like quantities having the same dimwnsions can be added to or substracted from each other.

✴ Solution :

$\bigstar\bf\:\red{[P]=[M^1L^{-1}T^{-2}]}\\ \\ \bigstar\bf\:\blue{[V]=[M^0L^3T^0]}\\ \\ \longrightarrow\sf\:[P]=\dfrac{[a]}{[V^2]}\\ \\ \longrightarrow\sf\:[a]=[P][V^2]\\ \\ \longrightarrow\boxed{\bf{\green{[a]=[M^1L^5T^{-2}]}}}\\ \\ \longrightarrow\sf\:[b]=[V]\\ \\ \longrightarrow\boxed{\bf{\pink{[b]=[L^3]}}}\\ \\ \longrightarrow\sf\:\dfrac{a}{b}=\dfrac{[M^1L^5T^{-2}]}{[L^3]}\\ \\ \longrightarrow\boxed{\bf{\purple{\dfrac{a}{b}=[M^1L^2T^{-2}]}}}$