Q.

The van der Waals' equation of state for some gases can be expressed as:P+aV2(V−b)=RTwhere P is the pressure, V is the molar volume, and T is the absolute temperature of the given sample of gas and a, b, and R are constants.The dimensions of a areThe dimensions of constant b areWhich of the following does not have the same dimensional formula as that for RT?The dimensional representation of ab/RT isIn the above problem, the dimensional formula for RT is same as that of

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a

ML5T−2

b

ML−1T−2

c

L3

d

L6

e

ML5T−2

f

ML−1T−2

g

L3

h

L6

i

PV

j

Pb

k

aV2

l

abV2

m

ML5T−2

n

M0L3T0

o

ML−1T−2

p

L6

q

Energy

r

Force

s

Specific heat

t

Latent heat

answer is , , , , .

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Detailed Solution

[a]=PV2=FV2A=MLT−2L6L2=ML5T−2[b]=[V]=L3According to given equation, PV+aV−Pb−abV2=RTAs dimensions of all the terms on LHS must be equal to dimensions of term RT on RHS, a/V2 does not have the same dimensional formula as that of RZ.abV2=[RT]⇒abRT=V2=L6[RT]=[PV]=FA⋅V=ML2T−2So the dimensional formula of RT is same as that of energy.
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The van der Waals' equation of state for some gases can be expressed as:P+aV2(V−b)=RTwhere P is the pressure, V is the molar volume, and T is the absolute temperature of the given sample of gas and a, b, and R are constants.The dimensions of a areThe dimensions of constant b areWhich of the following does not have the same dimensional formula as that for RT?The dimensional representation of ab/RT isIn the above problem, the dimensional formula for RT is same as that of