Vedclass

The equation of state of some gases can be expressed as $\left( {P + \frac{a}{{{V^2}}}} \right) = \frac{{b\theta }}{l}$ Where $P$ is the pressure, $V$ the volume, $\theta $ the absolute temperature and $a$ and $b$ are constants. The dimensional formula of $a$ is

  • [AIPMT 1996]
  • A

    $[M{L^5}{T^{ - 2}}]$

  • B

    $[{M^{ - 1}}{L^5}{T^{ 2}}]$

  • C

    $[M{L^{ - 5}}{T^{ - 1}}]$

  • D

    $[M{L^{ 5}}{T^{ 1}}]$

Similar Questions

Choose the correct match

List I 

List II

 $(i)$ Curie

 $(A)$ $ML{T^{ - 2}}$

 $(ii)$ Light year 

 $(B)$ $M$

 $(iii)$ Dielectric strength

 $(C)$ Dimensionless

 $(iv)$ Atomic weight

 $(D)$ $T$

 $(v)$ Decibel

 $(E)$ $M{L^2}{T^{ - 2}}$
 

 $(F)$ $M{T^{ - 3}}$
 

 $(G)$ ${T^{ - 1}}$
 

 $(H)$ $L$
 

 $(I)$ $ML{T^{ - 3}}{I^{ - 1}}$
 

 $(J)$ $L{T^{ - 1}}$

  • [IIT 1992]
View Solution

A new system of units is proposed in which unit of mass is $\alpha $ $kg$, unit of length $\beta $ $m$ and unit of time $\gamma $ $s$. How much will $5\,J$ measure in this new system ?

View Solution

Let $[{\varepsilon _0}]$ denotes the dimensional formula of the permittivity of the vacuum and $[{\mu _0}]$ that of the permeability of the vacuum. If $M = {\rm{mass}}$, $L = {\rm{length}}$, $T = {\rm{Time}}$ and $I = {\rm{electric current}}$, then

  • [IIT 1998]
View Solution

If force $(F)$, length $(L)  $ and time $(T)$ are assumed to be fundamental units, then the dimensional formula of the mass will be

View Solution

$\left(P+\frac{a}{V^2}\right)(V-b)=R T$ represents the equation of state of some gases. Where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a, b, R$ are the constants. The physical quantity, which has dimensional formula as that of $\frac{b^2}{a}$, will be

  • [JEE MAIN 2023]
View Solution