Inside a cylinder having insulating walls and | vedclass

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

Question

(D) Let the total volume of the cylinder be $V$. Let the volume occupied by the gas of mass $2m$ be $V_1$ and the volume occupied by the gas of mass $

Vedclass · Accepted Answer

$0.67$

Vedclass · Answer

(D) Let the total volume of the cylinder be $V$. Let the volume occupied by the gas of mass $2m$ be $V_1$ and the volume occupied by the gas of mass $m$ be $V_2 = V - V_1$.Since the piston is in equilibrium,the pressure $P$ on both sides is the same.Since the piston is conducting,the temperature $T$ is the same for both gases.Using the ideal gas equation $PV = nRT = \frac{m_{gas}}{M}RT$,where $M$ is the molar mass of the gas:For the gas with mass $m$: $P(V - V_1) = \frac{m}{M}RT$  $(i)$For the gas with mass $2m$: $P V_1 = \frac{2m}{M}RT$  $(ii)$Dividing equation $(ii)$ by equation $(i)$:$\frac{P V_1}{P(V - V_1)} = \frac{\frac{2m}{M}RT}{\frac{m}{M}RT}$$\frac{V_1}{V - V_1} = 2$$V_1 = 2V - 2V_1$$3V_1 = 2V$$\frac{V_1}{V} = \frac{2}{3} \approx 0.67$Thus,the larger mass occupies $0.67$ of the total volume.

Similar Questions

$A$ fixed amount of gas has a volume $V$ at constant pressure. If the temperature of the gas is increased such that the $v_{rms}$ of the molecules doubles,then its new volume will be .......

If the volume of a given mass of a gas is increased four times,and the temperature is raised from $27^{\circ}C$ to $127^{\circ}C$,what happens to its elasticity?

Air is filled in a bottle at atmospheric pressure and it is corked at $35^{\circ}C$. If the cork can come out at $3$ atmospheric pressure,then up to what temperature should the bottle be heated in order to remove the cork? (in $^{\circ}C$)

The volume of a given mass of a gas is increased by $7 \%$ at constant temperature. The pressure should be decreased by (in $\%$)

In Boyle's law, what remains constant?

Vedclass Test Series

Exam Paper Generator

Online Exam Module