Question

Relation between pressure ($P$) and energy density ($E$) of an ideal gas is-

• A. $P=2/3E$
• B. $P=3/2E$
• C. $P=3/5E$
• D. $P=E$

Answer 1

The correct option is A $P=2/3E$

Kinetic energy $=\frac{1}{2}{MV}_{rms}$

$\Rightarrow \frac{1}{2}M\left(\frac{3RT}{M}\right)$ $[M=$ molar mass,$V_{rms}=\sqrt{\frac{3KT}{m}}=\sqrt{\frac{3RT}{M}}]$

$=\frac{3}{2}RT$

$\Rightarrow K.E=\frac{3}{2}PV$ $[PV=RT]$

$\Rightarrow \frac{K.E}{V}=\frac{3}{2}P$

$\Rightarrow E=\frac{3P}{2}$ $E=$ Energy density.

Hence, the answer is $P=\frac{2}{3}E.$