Question

the root mean square velocity of a gas is C. if the pressure of the gas is doubled at constant temperature what will be the root mean square velocity of the gas sample

Answer 1

Answer:

According to Boyles law, PV = RT. Given T is constant. Hence, if P is doubled, V would be halved to keep RT constant.

Hence, Root mean square velocity = √RT/M will remain the same as RT is constant even if pressure is doubled.

Explanation:

Answer 2

Answer:

If the pressure of the gas is doubled, the root mean square velocity will remain the same.

Explanation:

Given,

The initial root mean square velocity of a gas = C.

The pressure of the gas is doubled

The temperature is constant.

The final root mean square velocity of the gas =?

As we know,

• The root mean square velocity, $V_{rms}$ = $\sqrt{\frac{3RT}{M} }$   -----equation (1)

Therefore, $\sqrt{\frac{3RT}{M} }$ = C ( as given )

Here,

• R = Raydberg's constant
• T = temperature
• M = molar mass

As we know,

• $PV = RT$    [ at n ( amount ) = 1 ]

According to Boyle's law, at a constant temperature,

• $PV = constant$

If pressure is doubled, the volume will be half to keep the temperature constant.

Therefore, pressure = 2P and the volume = $\frac{1}{2} V$

After putting the values in equation (1), we get:

• $V_{rms}$ = $\sqrt{\frac{3RT}{M} }$
• $V_{rms}$ = $\sqrt{\frac{3PV}{M} }$      ( PV = RT )

If pressure is doubled, the volume will be half;

• $V_{rms}$ = $\sqrt{\frac{3(2P)(\frac{V}{2}) }{M} }$
• $V_{rms}$ = $\sqrt{\frac{3PV}{M} }$ = $\sqrt{\frac{3RT}{M} }$ = C

Hence, the root mean square velocity will remain the same if the pressure of the gas is doubled.