The total kinetic energy of translatory motio | vedclass

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(C) The translational kinetic energy $(K.E._t)$ of an ideal gas is given by $K.E._t = \frac{3}{2} PV$.Given: $K.E._t = 3000 \, J$, $V = 5 \, L$, Press

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The total kinetic energy of $10 \, L$ of $O_2$ at a pressure of $2P$ is $20000 \, J$.

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(C) The translational kinetic energy $(K.E._t)$ of an ideal gas is given by $K.E._t = \frac{3}{2} PV$.Given: $K.E._t = 3000 \, J$, $V = 5 \, L$, Pressure $= P$.So, $3000 = \frac{3}{2} P(5) \Rightarrow P = \frac{3000 	imes 2}{15} = 400 \, J/L$.For option $(A)$: $N_2$ is a diatomic gas. Total $K.E. = \frac{5}{2} P'V' = \frac{5}{2} (2P)(10) = 50P = 50(400) = 20000 \, J$.For option $(B)$: $Ne$ is a monoatomic gas. Total $K.E. = \frac{3}{2} P'V' = \frac{3}{2} (2P)(1) = 3P = 3(400) = 1200 \, J$.For option $(C)$: $O_2$ is a diatomic gas. Total $K.E. = \frac{5}{2} P'V' = \frac{5}{2} (2P)(10) = 50P = 50(400) = 20000 \, J$.Thus, only the statement in option $(C)$ is correct.

The total kinetic energy of translatory motion of all the molecules of $5 \, L$ of nitrogen exerting a pressure $P$ is $3000 \, J$. Which of the following statements is correct?

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