Question 288: Thermodynamics & KTG

Question

$$\left(P+\frac{a}{V^{2}}\right)(V-b)=R T$$ represents the equation of state of some gases. Where $$P$$ is the pressure, $$V$$ is the volume, $$T$$ is the temperature and $$a, b, R$$ are the constants. The physical quantity, which has dimensional formula as that of $$\frac{b^{2}}{a}$$, will be:

Accepted Answer

$[a]=\left[\mathrm{ML}^{5} \mathrm{~T}^{-2}ight]$
$$
\begin{aligned}
& {[b]=\left[\mathrm{L}^{3}ight] } \\
& {\left[\frac{b^{2}}{a}ight]=\left[\frac{\mathrm{L}^{6}}{\mathrm{ML}^{5} \mathrm{~T}^{2}}ight] }=\left[\mathrm{M}^{-1} \mathrm{LT}^{-2}ight] \\
&=[	ext { Compressibility] }
\end{aligned}
$$

Answer

Energy density

Answer

Bulk modulus

Answer

Modulus of rigidity

Answer

Compressibility

Thermodynamics & KTG

\left(P+\frac{a}{V^{2}}\right)(V-b)=R T represents the equation of state of some gases. Where P is the pressure, V is the volume, T is the temperature and a, b, R are the constants. The physical quantity, which has dimensional formula as that of \frac{b^{2}}{a}$, will be:

Choose the correct answer: