Question
Question: The molecules of a given mass of a gas have a 'rms' velocity of \(200\;{\rm{m/s}}\) at \(27^\circ {\...
The molecules of a given mass of a gas have a 'rms' velocity of 200m/s at 27∘C and 1×105N/m2 pressure. When the temperature is 127∘C and pressure is 0.5×105N/m2. the rms velocity in m/swill be
- 31002
- 1002
- 3400
- 400
Solution
Here, we will be using the formula to find the root mean square velocity. The mean square velocity is independent of the pressure. So, we use the relation between the temperature and mean square velocity.
Complete step by step answer:
Given: The initial rms velocity of molecules is v1=200m/s, the initial temperature is T1=27∘C+273=300K, the final temperature is T2=127∘C+273=400K.
The formula for root mean square velocity is vrms=M3RT
Here, R is the universal gas constant, and M is the mass of a molecule.
From, above relative, we can write vrms∝T
Now, we write the relative formula for initial and final velocity using the above relation.
v2v1=T2T1
Here, v2 is the final velocity at 127∘C.
Substituting the values in above relation,