the absolute temperature of a gas is incresed 3 times. what will be the increase in rms velocity of the gas molecule?
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The root-mean-square speed urms of gas particles is given by the equation
urms=√3RTMM
where
R is the universal gas constant, for this case 8.314kg⋅m2s2⋅mol⋅K
T is the absolute temperature of the system, in K
MM is the molar mass of the gas, in kgmol
The question is nonspecific for which gas, but we're just asked to find what generally happens to the r.m.s. speed if only the temperature changes, so we'll call the quantity 3RMM a constant, k:
urms-1=√kT
If the temperature is tripled, then this becomes
urms-2=√3kT
To find what happens, let's divide this value by the original equation:
urms-2urms-1=√3kt√kt=√3
Thus, if the temperature is tripled, the root-mean-square speed of the gas particles increases by a factor of √3.
urms=√3RTMM
where
R is the universal gas constant, for this case 8.314kg⋅m2s2⋅mol⋅K
T is the absolute temperature of the system, in K
MM is the molar mass of the gas, in kgmol
The question is nonspecific for which gas, but we're just asked to find what generally happens to the r.m.s. speed if only the temperature changes, so we'll call the quantity 3RMM a constant, k:
urms-1=√kT
If the temperature is tripled, then this becomes
urms-2=√3kT
To find what happens, let's divide this value by the original equation:
urms-2urms-1=√3kt√kt=√3
Thus, if the temperature is tripled, the root-mean-square speed of the gas particles increases by a factor of √3.
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