Question:

In a vessel, the gas is at a pressure PP. If the mass of all the molecules is halved and their speed is doubled, then the resultant pressure will be

Updated On: Jul 28, 2022
  • P
  • 4 P
  • P/2
  • 2P
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The Correct Option is D

Solution and Explanation

Given: Initial pressure of the gas (P1)=P\left(P_{1}\right)=P; Initial mass of the gas molecules (m1)=m\left( m _{1}\right)= m; Final mass of gas molecules (m2)=0.5m;\left( m _{2}\right)=0 .5 \,m ; Initial speed of molecules (v1)=v\left(v_{1}\right)=v and final speed of the molecules (v2)=2v\left(v_{2}\right)=2 v. We know that pressure of the gas (P)=13×mnV×v2mv2(P)=\frac{1}{3} \times \frac{m n}{V} \times v^{2} \propto m v^{2} or P1P2=m1m2×(v1v2)2=10.5×(12)2=12\frac{P_{1}}{P_{2}}=\frac{m_{1}}{m_{2}} \times\left(\frac{v_{1}}{v_{2}}\right)^{2}=\frac{1}{0.5} \times\left(\frac{1}{2}\right)^{2}=\frac{1}{2} or P2=2P1P_{2}=2 P_{1}. ...(where P2P_{2} is the resultant pressure).
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