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Previous Years JEE Advanced Questions
Q. A real gas behaves like an ideal gas if its ?
(A) pressure and temperature are both high
(B) pressure and temperature are both low
(C) pressure is high and temperature is low
(D) pressure is low and temperature is high
Ans. (D)
$\operatorname{High} \vec{P},$ Low $P$
Q. A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic
mass = 40 amu) is kept at 300 K in a container. The ratio of the rms speeds $\left(\frac{v_{r m s}(\text {helium})}{v_{r m s}(\text {arg on})}\right)$ is ?
(A) 0.32 (B) 0.45 (C) 2.24 (D) 3.16
[JEE-2012]
Ans. (D)
$v_{m s}=\sqrt{\frac{3 R T}{M}} ; \frac{\left(v_{m s}\right)_{H e}}{\left(v_{m s}\right)_{A r}}=\sqrt{\frac{M_{A r}}{M_{H e}}}=\sqrt{\frac{40}{4}}=\sqrt{10}=3.16$
Q. Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is :-
(A) 1 : 4 (B) 1 : 2 (C) 6 : 9 (D) 8 : 9
[JEE-2013]
Ans. (D)
$\mathrm{P}=\frac{\rho}{\mathrm{M}} \mathrm{RT}$
$\Rightarrow \frac{\mathrm{P}_{1}}{\mathrm{P}_{2}}=\frac{\rho_{1} \mathrm{M}_{2}}{\rho_{2} \mathrm{M}_{1}}=\frac{4}{3} \Rightarrow \frac{\rho_{1}}{\rho_{2}}=\frac{4}{3} \times \frac{2}{3}=\frac{8}{9}$
Q. A container of fixed volume has a mixutre of one mole of hydrogen and one mole of helium in equilibrium at temperature T. Assuming the gases are ideal, the correct statement(s) is (are) :-
(A) The average energy per mole of the gas mixture is 2RT.
(B) The ratio of speed of sound in the gas mixture to that in helium gas is $\sqrt{6 / 5}$.
(C) The ratio of the rms speed of helium atoms to that of hydrogen molecules is 1/2.
(D) The ratio of the rms speed of helium atoms to that of hydrogen molecules is $1 / \sqrt{2}$.
[JEE-Advance-2015]
Ans. (A,B,D)
$C_{V(\operatorname{mix})}=\frac{(1)\left(\frac{3}{2} R\right)+(1)\left(\frac{5}{2} R\right)}{2}=2 R$
$\mathrm{C}_{\mathrm{P}(\mathrm{mix})}=3 \mathrm{R} \quad \gamma_{\operatorname{mix}}=\frac{3}{2} \Rightarrow \mathrm{f}=4$
Average energy/mole $=\mathrm{f} \frac{1}{2} \mathrm{RT}=2 \mathrm{RT}$
$\frac{\left(\mathrm{V}_{\mathrm{sound}}\right)_{\mathrm{mixture}}}{\left(\mathrm{V}_{\mathrm{sound}}\right)_{\mathrm{He}}}=\frac{\sqrt{\frac{\mathrm{RT}}{2}}}{\sqrt{\frac{5 \mathrm{RT}}{12}}}=\sqrt{\frac{6}{5}}$
$\frac{\left(\mathrm{V}_{\mathrm{rms}}\right)_{\mathrm{He}}}{\left(\mathrm{V}_{\mathrm{rms}}\right)_{\mathrm{H}_{2}}}=\frac{\sqrt{\frac{3 \mathrm{RT}}{4}}}{\sqrt{\frac{3 \mathrm{RT}}{2}}}=\frac{1}{\sqrt{2}}$
$\therefore(\mathrm{A}, \mathrm{B}, \mathrm{D})$