A closed vessel contains 10 g of an ideal ga | vedclass

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

Question

(D) For an ideal gas,the ideal gas equation is $PV = nRT$.Since $T$ and $V$ are constant,$n \propto P$.Let $n_X$ and $n_Y$ be the number of moles of g

Vedclass · Accepted Answer

$2: 1$

Vedclass · Answer

(D) For an ideal gas,the ideal gas equation is $PV = nRT$.Since $T$ and $V$ are constant,$n \propto P$.Let $n_X$ and $n_Y$ be the number of moles of gases $X$ and $Y$ respectively.For gas $X$: $n_X = \frac{10}{M_X} \propto 2 \ atm$  ---$(1)$When gas $Y$ is added,the total pressure becomes $6 \ atm$. The pressure due to gas $Y$ is $6 - 2 = 4 \ atm$.For gas $Y$: $n_Y = \frac{80}{M_Y} \propto 4 \ atm$  ---$(2)$Dividing equation $(1)$ by $(2)$:$\frac{10/M_X}{80/M_Y} = \frac{2}{4} \Rightarrow \frac{10}{M_X} 	imes \frac{M_Y}{80} = \frac{1}{2} \Rightarrow \frac{M_Y}{8M_X} = \frac{1}{2} \Rightarrow \frac{M_Y}{M_X} = 4$.The root mean square velocity is given by $V_{rms} = \sqrt{\frac{3RT}{M}}$,so $V_{rms} \propto \frac{1}{\sqrt{M}}$.Therefore,$\frac{(V_{rms})_X}{(V_{rms})_Y} = \sqrt{\frac{M_Y}{M_X}} = \sqrt{4} = 2$.The ratio is $2:1$.

$A$ closed vessel contains $10 \ g$ of an ideal gas $X$ at $300 \ K$,which exerts $2 \ atm$ pressure. At the same temperature,$80 \ g$ of another ideal gas $Y$ is added to it and the pressure becomes $6 \ atm$. The ratio of root mean square velocities of $X$ and $Y$ at $300 \ K$ is

Similar Questions

$A$ box contains $N$ molecules of a perfect gas at temperature ${T_1}$ and pressure ${P_1}$. The number of molecules in the box is doubled while keeping the total kinetic energy of the gas the same as before. If the new pressure is ${P_2}$ and temperature is ${T_2}$,then:

$A$ light container having a diatomic gas enclosed within is moving with velocity $v$. The mass of the gas is $M$ and the number of moles is $n$. The kinetic energy of the gas with respect to the ground is:

$A$ thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $\gamma$. It is moving with speed $v$ and it is suddenly brought to rest. Assuming no heat is lost to the surroundings,its temperature increases by

An ideal gas $(\gamma = 1.5)$ is expanded adiabatically. How many times must the gas be expanded to reduce the root mean square velocity of the molecules $2.0$ times?

Vedclass Test Series

Exam Paper Generator

Online Exam Module