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