There are n molecules of a gas in a box. If the number of molecules is

1.	There are n molecules of a gas in a box. If the number of molecules is increased to 2n, what will be the effect on the pressure of the gas? On the total energy of the gas? On the root-mean-square speed of the molecules?
Answer» Since, P = \(\frac{1}{3}\frac{mnc^2}{V}\), i.e., P ∝ n, Therefore, pressure will be double when number of molecules n becomes 2n. As kinetic energy of the gas = \(\frac{1}{2}mnc^2\) , Therefore, K.E. of the gas also becomes double when n changes to 2n. Since, r.m.s. velocity of molecules of a gas only depends upon the temperature, hence, r.m.s. velocity of the molecules will remain the same when n changes to 2n.

There are n molecules of a gas in a box. If the number of molecules is increased to 2n, what will be the effect on the pressure of the gas? On the total energy of the gas? On the root-mean-square speed of the molecules?

Answer»

Since,

P = \(\frac{1}{3}\frac{mnc^2}{V}\),

i.e., P ∝ n,

Therefore, pressure will be double when number of molecules n becomes 2n. As kinetic energy of the gas = \(\frac{1}{2}mnc^2\) ,

Therefore, K.E. of the gas also becomes double when n changes to 2n. Since, r.m.s. velocity of molecules of a gas only depends upon the temperature, hence, r.m.s. velocity of the molecules will remain the same when n changes to 2n.

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There are n molecules of a gas in a box. If the number of molecules is increased to 2n, what will be the effect on the pressure of the gas? On the total energy of the gas? On the root-mean-square speed of the molecules?

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