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Byju's Answer

Standard IX

Chemistry

Experiment for Pressure and Volume Relationship

In the equati...

Question

In the equation $P = \frac{R T}{V - b} e^{\frac{a V}{R T}}$
$V = v o l u m e, P = p r e s s u r e, R =$ universal gas constant, and $T =$ temperature
The dimensional formula of $a$ is same as that of

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Solution

The correct option is B P
From the equation, $\frac{a V}{R T}$ should be dimensionless.
We know that RT has the same dimension as of PV, from the ideal gas equation.
Hence, the dimension of 'a' should be equal to Pressure.

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Similar questions

Q. Given that

P = \frac{R T}{V - b} e^{\frac{- a V}{R T}} .

The dimensional formula of

a

is same as that of:

(

V

=

volume,

T

=

temperature,

P

=

pressure,

R

=

universal gas constant)

Q. The pressure of a gas

P = \frac{R T}{v - b} e^{⎛ ⎝ \frac{- a V}{R T} ⎞ ⎠}

. If

V

be the volume of gas,

R

be the universal gas constant and

T

be the absolute temperature then the dimensional formula of '

a

' is same as that of:

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. 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.

Comprhension:
The van der Waal's gas equation is

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

, where

P

is the pressure,

V

is molar volume and

T

is the temperature of the given sample of gas.

R

is called molar gas constant,

a

and

b

are called van der Waal's constants.

The dimensional formula for

a

is same as that for

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In the equation P=RTV−beaVRTV=volume,P=pressure,R= universal gas constant, and T= temperatureThe dimensional formula of a is same as that of

The correct option is B PFrom the equation, aVRT should be dimensionless.We know that RT has the same dimension as of PV, from the ideal gas equation.Hence, the dimension of 'a' should be equal to Pressure.

In the equation $P = \frac{R T}{V - b} e^{\frac{a V}{R T}}$
$V = v o l u m e, P = p r e s s u r e, R =$ universal gas constant, and $T =$ temperature
The dimensional formula of $a$ is same as that of

The correct option is B P
From the equation, $\frac{a V}{R T}$ should be dimensionless.
We know that RT has the same dimension as of PV, from the ideal gas equation.
Hence, the dimension of 'a' should be equal to Pressure.