A) The fraction of molecules having speeds in the range of u to \[u+du\] of a gas of molar mass, Mat temperature Tis the same as that of the gas of molar mass 2M at temperature\[T/2\].
B) The product of pressure and volume of a fixed mass of a gas is independent of temperature.
C) Rise in compressibility factor with increasing pressure is due to van der Waal's constant b.
D) All molecules in a gas are moving with the same speed.
Correct Answer: C
Solution :
[c] Statement (1) is INCORRECT Since \[\frac{1}{N}\frac{dN}{du}=4\pi \left( \frac{M}{2\pi RT} \right){{u}^{2}}{{e}^{(-m{{u}^{2/2RT}})}}\] This will be so if temperature of the gas of molar mass 2M is 2T Statement (2) is INCORRECT According to Boyle's Law, the product .of pressure and volume depends upon temperature Statement (3) is CORRECT. This is due to factor 'b' not 'a' Since. \[\left( p+\frac{a}{{{V}^{2}}m} \right)({{V}_{m}}-b)=RT\] Neglecting \[(a/{{V}^{2}}m),\] we get \[pVm-pb=RT\] Divide by RT, we get, \[\frac{pVm}{RT}-\frac{pb}{RT}=\frac{RT}{RT}\] \[Z=1+\frac{pb}{RT}\] Statement (4) is INCORRECT Movements of molecules in a gas follow Maxwell's distribution Law.
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