You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

1st Law of Thermodynamics

The equation ...

Question

The equation of state of a real gas is given by $(P = \frac{a}{V^{2}}) (V - b) = R T$ , where P, V and T are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of the constant a in the given equation is _______.

M L^{6} T^{- 2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

M L^{5} T^{- 2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

M L^{7} T^{- 2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

M L^{8} T^{- 2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $M L^{5} T^{- 2}$ .
Dimension of P = Dimension of $(\frac{a}{V^{2}})$
$\Rightarrow M L^{- 1} T^{- 2} = \frac{Dimension of a}{L^{6}}$
$\Rightarrow Dimension of a = M L^{5} T^{- 2}$
Hence, option B is correct.

Suggest Corrections

Similar questions

Q. The equation of state for a gas is given by

(P + \frac{a}{V^{2}}) (V - b) = R T

,
where

P

V

and

T

are pressure, volume and temperature respectively and

R

is the universal gas constant. The dimensions of the constant

a

Q. Find dimensions of constants

a

and

b

in equation.

(P + \frac{a}{V^{2}}) (V - b) = R T

, where

P

is pressure and

V

is volume,

R

is universal gas constant,

T

is temperature.

Q. The dimensions of '

a

' in Vanderwaal's equation

(P + \frac{a}{V^{2}}) (V - b) = R T

is:

(

V

-volume,

P

-Pressure,

R

-Universal gas constant,

T

- Temperature)

Q. The Vander waal's equation for ideal gas is given by

(p + \frac{a}{V^{2}}) (V - b) = R T

where

P

is pressure,

V

is volume

a

and

b

are constants,

R

is universal gas constant and

T

is absolute temperature. Then the dimensions of

\frac{a}{b}

are same as that of:

Q. The equation of state of a gas is given by

(\begin{matrix} P + \frac{a}{v^{3}} \end{matrix}) (V - b^{2}) = c T

, where P, V, T are pressure, volume and temperature respectively, and a, b, c are constants. The dimensions of a and b are respectively

Join BYJU'S Learning Program

The equation of state of a real gas is given by (P=aV2)(V−b)=RT, where P, V and T are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of the constant a in the given equation is _______.

The correct option is B ML5T−2.Dimension of P = Dimension of (aV2)⇒ML−1T−2= Dimension of aL6⇒Dimension of a=ML5T−2Hence, option B is correct.

The equation of state of a real gas is given by $(P = \frac{a}{V^{2}}) (V - b) = R T$ , where P, V and T are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of the constant a in the given equation is _______.

The correct option is B $M L^{5} T^{- 2}$ .
Dimension of P = Dimension of $(\frac{a}{V^{2}})$
$\Rightarrow M L^{- 1} T^{- 2} = \frac{Dimension of a}{L^{6}}$
$\Rightarrow Dimension of a = M L^{5} T^{- 2}$
Hence, option B is correct.