I've been asked to find the temperature to which a 20.0°C gas must be raised to increase its root mean square (rms) speed by a given percentage. Is this possible without knowing the identity of the gas?

Asked by HeroicZach (195

) August 26th, 2009

Some help with how to attack problems like these would be really helpful (I’d be forever in your debt – you know, like in Harry Potter, it would be like one of those super-swears they have).

The problem basically tells me I have to raise the rms speed of the molecules in “a gas” by 1.0%, I have it at 20.0°C, and I need to find what temperature it should be at to have the given rms speed. As far as I know, you would have to know what gas it is, since the rms speed formula is sqrt(3RT/m), m being the molecular mass of one of the gas particles in kg (calculated by using Boltzmann’s constant and the molar mass on the periodic table).

Help?

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4 Answers

Pretend the gas is hydrogen. Work out the problem.

Pretend the gas is oxygen. Work out the problem.

Are the answers you get any different?

cwilbur (14236

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@cwilbur Thank you for your help =). My answer matches the one in the back of the book no matter which gas I use, so it looks like I’m doing something right! I guess as long as you keep m constant it’s irrelevant.

HeroicZach (195

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Now, the important question is: do you understand why m doesn’t matter, so long as it’s constant?

cwilbur (14236

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The equation is poised like this
V1=Sqrt(3R20/m) V2=101V1/100=Sqrt(3RT/m)

v2/v1=101/100=sqrt(3RT/m/3R20/m)

=sqrt(T/20)=101/100 all other parameters gets cancelled out.
So,no need to bother about the identity of the gas while dealing with such problems.
Just use the formula
V2/V1=sqrt(T2/T1)
Remember,this hold true only for finding the RMS value of the of the velocity of gas.

engineeristerminatorisWOLV (687

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