Kinetic Theory - Result Question 14
14. In a vessel, the gas is at a pressure $P$. If the mass of all the molecules is halved and their speed is doubled, then the resultant pressure will be
(a) $4 P$
(b) $2 P$
(c) $P$
(d) $P / 2$
[NEET Kar: 2013]
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Answer:
Correct Answer: 14. (b)
Solution:
- (b) $\because P=\frac{1}{3} \frac{m N}{V} v_rms^{2}$
where $m=$ mass of each molecules
$N=$ total number of molecules
$V=$ volume of the gas
When mass is halved and speed is doubled then
Resultant pressure, $P^{\prime}=\frac{1}{3} \times(\frac{m}{2}) \times \frac{N}{V}(2 v _{rms})^{2}$
$ =2 P $
