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RMS speed of ideal gas molecules is , where T is the temperature in kelvin, R is universal gas constant,M is the molar mass of gas. ratio of rms speeds of molecules at T2 and T1 is = …..(1)Now, we need to compute temperatures T1 and T2.We know that for isotherm, PV = constant i.e. PV = nRT and T is constant.Consider isotherm at T1. It is passing through P = 1.105 Pa and V = 1 m3.So, 1.105 Pa . 1 m3 = nR T1 or T1 = (105 / nR) KSimilarly, for T2, P = 2.105 Pa and V = 2 m3.So, 2.105 Pa . 2 m3 = nR T2 or T2 = (4.105 / nR) KSubstitute value of T1 and T2 in (1) and you will getratio of rms speeds = = 2 .
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