If P represents the pressure exerted by an ideal gas and E represents the translational kinetic energy per unit volume of the gas, then

Question

If P represents the pressure exerted by an ideal gas and E represents the translational kinetic energy per unit volume of the gas, then (A) P = E (B) P = 2E (C) P = 3E (D) P= (2/3)E

Tardigrade Admin · Accepted Answer

P=(1/3) (m N v ms 2/V) =(2/3)((1/2)(m N) v ms 2) ⋅ (1/V)=(2/3)((K E/V)) ⇒ P=(2 E/3)

Q. If $P$ represents the pressure exerted by an ideal gas and $E$ represents the translational kinetic energy per unit volume of the gas, then

P = E

P = 2E

P = 3E

$P = \frac{2}{3} E$

$P = \frac{1}{3} \frac{m N v _{m s}^{2}}{V}$
$= \frac{2}{3} (\frac{1}{2} (m N) v_{m s}^{2}) \cdot \frac{1}{V} = \frac{2}{3} (\frac{K E}{V})$
$\Rightarrow P = \frac{2 E}{3}$

Q. If P represents the pressure exerted by an ideal gas and E represents the translational kinetic energy per unit volume of the gas, then