Question

The Van der Waal's equation of state for some gases can be expressed as:
$(P+\frac{a}{V^2})(V-b)=RT$
where 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.
In the above problem, the dimensional formula for RT is same as that of

• A. Energy
• B. Force
• C. Specific heat
• D. Latent heat

Answer 1

The correct option is A Energy

$\left[RT\right]=\left[P\right]\left[V\right]$ [From given equation]

$\Rightarrow \left[RT\right]=\left[{ML}^{-1}{T}^{-2}\right]\left[L^3\right]$

$\Rightarrow \left[RT\right]=\left[{ML}^2{T}^{-2}\right]$

Now,

$\left[Energy\right]=[Force\times displacement]=\left[{MLT}^{-2}\right]\left[L\right]$

$\left[Energy\right]=\left[{ML}^2{T}^{-2}\right]=\left[RT\right]$