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)

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 $\left(m_2\right)=0.5m;$ Initial speed of molecules $\left(v_1\right)=v$ and final speed of the molecules $\left(v_2\right)=2v$.
We know that pressure of the gas $(P)=\frac{1}{3}\times \frac{mn}{V}\times v^2\propto m{v}^2$
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 $P_2=2P_1$.
...(where $P_2$ is the resultant pressure).