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Question

The equation of state of a real gas can be expressed as (P+aV2)(V−b)=cT, where P is the pressure, V the volume, T the absolute temperature and a, b, c are constants. What are the dimensions of 'a'-

A
M0L3T2
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B
ML2T5
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C
ML5T2
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D
M0L3T0
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Solution

The correct option is C ML5T2
(p+aV2)(vb)=cT
p is pressure, V is volume and T is temperature
p=FA=MLT2L2=ML1T2V=L3
We cannot add or subtract quantities of different dimensions.
p=aV2a=pV2=ML1T2(L3)2=ML5T2
Hence, Option C is correct.

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