Question

The total kinetic energy of translatory motion of all molecules of 5 litres of nitrogen exerting a pressure is 3000J

• A. the total K.e of 10 litres of $N_2$ at pressure of 2P is 3000J
• B. the total K.e of 10 litres of $He$ at pressure of 2P is 3000J
• C. the total K.e of 10 litres of $O_2$ at pressure of 2P is 20000J
• D. the total K.e of 10 litres of $Ne$ at pressure of 2P is 12000J

Answer 1

Answer: (C), (D)

The correct options are
C the total K.e of 10 litres of $O_2$ at pressure of 2P is 20000J
D the total K.e of 10 litres of $Ne$ at pressure of 2P is 12000J

Total energy of gas $E=\frac{f}{2}PV$
where $f=\text{degree of freedom}$
Total kinetic energy of translatory motion of 5 litres of nitrogen exerting at a pressure P is 3000J,
$f=3\left(fortranslatorymotion\right)$
$\frac{3}{2}\times P\times 5\times {10}^{-3}=3000$
$P=400\times {10}^{3}N/m^2$
(a) the total K.e of 10 litres of $N_2$ at pressure of 2P is 3000J
f = 5
$E=\frac{5}{2}\times (2\times 400\times {10}^3)\times (10\times {10}^{-3})$
$E=20000J$
false
(b)the total K.e of 10 litres of He at pressure of 2P is 3000J
f = 3
$E=\frac{3}{2}\times (2\times 400\times {10}^3)\times (10\times {10}^{-3})$
$E=12000J$
false
(c)the total K.e of 10 litres of $O_2$ at pressure of 2P is 20000J
f = 5
$E=\frac{5}{2}\times (2\times 400\times {10}^3)\times (10\times {10}^{-3})$
$E=20000J$
false
(d)the total K.e of 10 litres of Ne at pressure of 2P is 12000J
f = 3
$E=\frac{3}{2}\times (2\times 400\times {10}^3)\times (10\times {10}^{-3})$
$E=12000J$
false

answer is C,D.