Answer:
The new rms speed is 1.414 times the original rms speed
Explanation:
The rms speed (root-mean-square speed) of the molecules in a gas can be found by using the formula:
[tex]v=\sqrt{\frac{3RT}{M}}[/tex]
where
R is the gas constant
T is the absoolute temperature (in Kelvin) of the gas
M is the molar mass of the gas (the amount of mass per unit mole)
We can rewrite the equation as
[tex]v\propto \sqrt{T}[/tex] (1)
which means that the rms speed is proportional to the square root of the temperature.
In this problem, we are told that the absolute temperature of the gas is doubled, so the new temperature is
[tex]T'=2T[/tex]
Therefore, according to eq(1), we find that the new rms speed will be:
[tex]v\propto \sqrt{T'} = \sqrt{2T}=\sqrt{2} \sqrt{T}=\sqrt{2}v=1.414v[/tex]
So,
The new rms speed is 1.414 times the original rms speed
If the absolute temperature of a gas is doubled ; ( D ) The new rms speed is 1.414 times the original rms speed
The r.m.s speed of molecules in a gas can be calculated using the formula below ;
[tex]v = \sqrt{\frac{3RT}{M} }[/tex]
T = absolute temperature
R = gas constant
M = molar mass
Also ; The rms speed of gas molecules is directly proportional to [tex]\sqrt{T}[/tex]
i.e. v ∝ √T ----- ( 1 )
Given that the absolute temperature ( T ) is doubled the new value of T = 2T
Back to equation ( 1 )
v = √2T = √2 * √T
= 1.414
Hence we can conclude that If the absolute temperature of a gas is doubled The new rms speed is 1.414 times the original rms speed.
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