Two identical containers A and B with frictio | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The initial pressure in the two containers is given by the ideal gas law $PV = nRT = (m/M)RT$,where $M$ is the molar mass.$P_A = \frac{m_A RT}{MV}

Vedclass · Accepted Answer

$3m_A = 2m_B$

Vedclass · Answer

(C) The initial pressure in the two containers is given by the ideal gas law $PV = nRT = (m/M)RT$,where $M$ is the molar mass.$P_A = \frac{m_A RT}{MV}$ and $P_B = \frac{m_B RT}{MV}$.After isothermal expansion to volume $2V$,the final pressures are:$P'_A = \frac{m_A RT}{M(2V)}$ and $P'_B = \frac{m_B RT}{M(2V)}$.The change in pressure for each container is:$\Delta P_A = P_A - P'_A = \frac{m_A RT}{MV} - \frac{m_A RT}{2MV} = \frac{m_A RT}{2MV}$.$\Delta P_B = P_B - P'_B = \frac{m_B RT}{MV} - \frac{m_B RT}{2MV} = \frac{m_B RT}{2MV}$.Given that $\Delta P_A = \Delta P$ and $\Delta P_B = 1.5 \Delta P$,we take the ratio:$\frac{\Delta P_A}{\Delta P_B} = \frac{\Delta P}{1.5 \Delta P} = \frac{1}{1.5} = \frac{2}{3}$.Substituting the expressions for $\Delta P_A$ and $\Delta P_B$:$\frac{m_A RT / 2MV}{m_B RT / 2MV} = \frac{2}{3} \implies \frac{m_A}{m_B} = \frac{2}{3}$.Therefore,$3m_A = 2m_B$.

Similar Questions

The efficiency of a Carnot engine is $50\%$ and the temperature of the sink is $500\, K$. If the temperature of the source is kept constant and its efficiency is to be raised to $60\%$,then the required temperature of the sink will be........ $K$.

The mid-point of a chord of the ellipse $x^2+4y^2-2x+20y=0$ is $(2, -4)$. The equation of the chord is

The same current is flowing in two alternating circuits. The first circuit contains only an inductor and the second contains only a capacitor. If the frequency of the $e.m.f.$ of the $ac$ source is increased,what will be the effect on the value of the current in these circuits?

$A$ river of salty water is flowing with a velocity $2 ~m/s$. If the density of the water is $1.2 ~g/cc$,then the kinetic energy of each cubic metre of water is

$A$ conveyor belt is moving at a constant speed of $2\, m/s$. $A$ box is gently dropped on it. The coefficient of friction between them is $\mu = 0.5$. The distance that the box will move relative to the belt before coming to rest on it,taking $g = 10\, m/s^2$,is ........ $m$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module