A) \[\frac{1}{3}\rho \,{{\bar{c}}^{2}}\]
B) \[\frac{1}{3}\rho {{(c+v)}^{2}}\]
C) \[\frac{1}{3}\rho {{(\bar{c}-v)}^{2}}\]
D) \[\frac{1}{3}\rho {{({{c}^{-2}}-v)}^{2}}\]
Correct Answer: A
Solution :
[a] Pressure of the gas will not affected by motion of the system, hence by \[{{v}_{rms}}=\sqrt{\frac{3P}{\rho }}\]Þ \[{{\bar{c}}^{2}}=\frac{3P}{\rho }\]Þ\[P=\frac{1}{3}\rho {{\bar{c}}^{2}}\]
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