The average speed at T1 K and the most probable speed at T2 K of CO2 gas is 9×104cms−. Calculatethe value of T1

Mol. wt., M of CO2=12+(2×16)=44gmol−R=8.314×107gcm2s−2mol−Average speed Uav atT1=8RT1πM1/2and most probable speedUmp at T2=2RT2M1/2 are equal forCO2 (given)∴ 8RT1πM1/2=2RT2M1/2;8RT1πM=2RT2M4π=T2T1                                                       ….(A) (ii)    Ump=2RTM1/29×104=2×8.314×107gcm2s−2mol−T244gmol−1/2[∴ Mol. wt. of CO2=12+(2×16)=44gmolSquaring both sides, we get : 9×104cms−×9×104cms−=2×8.314×107cm2s−2×T2/44∴ T2=9×104×9×104×442×8.314×107= 2143.37 KSince, 4π=T2T1 see equation (A),So, 43.142=2143.37T1      T1=2143.37×3.1424=1683.6K