Three moles of Helium gas start at atmospheric pressure and

Three moles of Helium gas start at atmospheric pressure and a temperature of 260 C . The volume is then reduced to one half of its original value at constant pressure, then the pressure is tripled at constant volume. Find the rms speed in the final stae in m/s.

Solution

ideal gas equation:

PV = nRT

Then,

   P1V1/T1 = P2V2/T2

So, the new temperature is,

P(V/2)/T1 = 3P*V/T2

   1/2T1 = 3/T2

    1/2*(260+273) = 3/T2

      T2 = 3198 K

vrms = sqrt[3RT/M] = sqrt[3*8.314*3198 / 4.002x10^-3 kg/mol] = 4.46e+3 m/s