Question

# The equation of state of a gas is given by $$\left( p+\cfrac { a }{ { V }^{ 3 } } \right) \left( V-{ b }^{ 2 } \right) =cT$$, where $$p,V,T$$ are pressure, volume and temperature respectively and $$a,b,c$$ are constants. The dimensions of $$a$$ and $$b$$ are respectively:

A
[ML8T2andL3/2]
B
[ML5T2andL3]
C
[ML8T2andL6]
D
[ML6T2andL3/2]

Solution

## The correct option is B $$\left[ M{ L }^{ 8 }{ T }^{ -2 }\quad and\quad { L }^{ 3/2 } \right]$$$$\left[ P \right] =\left[ \cfrac { a }{ { V }^{ 3 } } \right] \Rightarrow \left[ M{ L }^{ -1 }{ T }^{ -2 } \right] =\cfrac { a }{ { \left[ { L }^{ 3 } \right] }^{ 3 } }$$$$\Rightarrow$$ $$a=\left[ M{ L }^{ 8 }{ T }^{ -2 } \right]$$$$\left[ V \right] =\left[ { b }^{ 2 } \right] \Rightarrow \left[ { L }^{ 3 } \right] ={ b }^{ 2 }\Rightarrow b=\left[ { L }^{ 3/2 } \right]$$Physics

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