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

$A$ container $A$ contains an ideal gas at pressure $P$,volume $V$,and temperature $T$. $A$ second container $B$ contains the same gas at pressure $2P$,volume $2V$,and temperature $\frac{T}{2}$. The ratio of the mass of gas in $A$ to that in $B$ is:

What is Avogadro number? Write its value.

$1$ mole of gas occupies a volume of $100\, ml$ at $50\, mm$ pressure. What is the volume occupied by two moles of gas at $100\, mm$ pressure and at the same temperature? (in $ml$)

At $0\,^{\circ}\text{C}$,the value of the density of a fixed mass of an ideal gas divided by its pressure is $x$. At $100\,^{\circ}\text{C}$,this quotient is:

The temperature of a gas at pressure $P$ and volume $V$ is $27^{\circ}C$. Keeping its volume constant,if its temperature is raised to $927^{\circ}C$,then its pressure will be (in $P$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module