A mixture contains 8g He and 14 g Nin a vessel at 300k. how much heat (in terms of R) is required to increase the rms speeds of these molecules to become the double their initial values? also calculate the final temperatures

Dear Student,

vrms=3RTMInitial temperature, T1= 300 KLet the initial rms velocity= vGiven that rms velocity at T2 is twice, so final rms velocity=2vhere, 3RM is constantTherefore, vrms1vrms2=T1T2or, T1T2=(v2v)2or, T2= 4T1= 4×300=1200 Kand, U=32nRTHere, n=moles of He+moles of N2= 84+1414=2+1=3or, U=32nRTor, U=32×3×R×(1200-300)=92×R×900or, U=4050R            

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