Question

The equation of state of some gases can be
expressed as (P+a/v2) (v-b) =RT. Here P is
the pressure, V is the volume T is the absolute
temperature and a,b, R are constants. The
dimensions of 'a'are:
a) ML5T-2
b) ML-2T-2.
d) MºL6T0
c) M0L3T0​

Answer 1

Answer:

b)$ML^2T^{-2}$

Explanation:

Given:

The equation of state of the gas as follow

$(P+\dfrac{a}{2V})+(V-b)=RT$

We know that operations such such as addition or subtraction can be done when they have dimension.

Here in the equation the dimension of P is same as that of $\dfrac{a}{2V}$

let the dimension a be $M^aL^bT^c$

Dimension of P is$M^1L^{-1}T^{-2}$

Dimension of V is $L^3$

According to question we have

$M^1L^{-1}T^{-2}= M^aL^{b-3}T^c$

By comparing we have

a=1

b=2

c=-2

So the dimension of a is  $M^1L^2T^{-2}$

The correct option is b.

Answer 2

Answer:

correct answer ......is b