Question

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. P
• B. 4 P
• C. P/2
• D. 2P

Answer 1

Answer: (D)

2P

Answer 2

Given: Initial pressure of the gas $\left(P_{1}\right)=P$; Initial mass of the gas molecules $\left( m _{1}\right)= m$; Final mass of gas molecules $\left( m _{2}\right)=0 .5 \,m ;$ Initial speed of molecules $\left(v_{1}\right)=v$ and final speed of the molecules $\left(v_{2}\right)=2 v$. We know that pressure of the gas $(P)=\frac{1}{3} \times \frac{m n}{V} \times v^{2} \propto m v^{2}$ or $\frac{P_{1}}{P_{2}}=\frac{m_{1}}{m_{2}} \times\left(\frac{v_{1}}{v_{2}}\right)^{2}=\frac{1}{0.5} \times\left(\frac{1}{2}\right)^{2}=\frac{1}{2}$ or $P_{2}=2 P_{1}$. ...(where $P_{2}$ is the resultant pressure).