JEE Main 2021 — Physics Thermodynamics

2021mcqmedium

A mixture of hydrogen and oxygen has volume $500{\mathrm{cm}}^{3},$ temperature $300K,$ pressure $400k\mathrm{Pa}$ and mass $0.76g.$ The ratio of masses of oxygen to hydrogen will be:

Official previous-year question

Held on 31 Aug 2021 · Verified 6 Jul 2026.

Options

A
$16:3$
B
$3:8$
C
$8:3$
D
$3:16$

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Solution

A number of moles of, ${O}_{2}=\frac{{m}_{1}}{32}$ , the number of moles of, ${H}_{2}=\frac{{m}_{2}}{2}$ . Using the ideal gas equation, $PV=[\frac{{m}_{1}}{32}+\frac{{m}_{2}}{2}]\frac{25}{3}\times 300$ ,

$400\times {10}^{3}\times 500\times {10}^{-6}=[\frac{{m}_{1}}{32}+\frac{{m}_{2}}{2}]25\times 100 \Rightarrow 2\times {10}^{2}=[\frac{{m}_{1}}{{m}_{2}}\times \frac{1}{32}+\frac{1}{2}]{m}_{2}\times 25\times 100$

$\Rightarrow \frac{2}{25}=[\frac{{m}_{1}}{{m}_{2}}\times \frac{1}{32}+\frac{1}{2}]{m}_{2}...(1)$

$\Rightarrow {m}_{1}+{m}_{2}=0.76$

$\Rightarrow {m}_{2}[1+\frac{{m}_{1}}{{m}_{2}}]=\frac{76}{100}...(2)$

$(1)$ divided by $(2)$ ; $\frac{[\frac{{m}_{1}}{{m}_{2}}\times \frac{1}{32}+\frac{1}{2}]}{[\frac{{m}_{1}}{{m}_{2}}+1]}=\frac{2}{25}\times \frac{100}{76}$

Let assume,

$\Rightarrow \frac{{m}_{1}}{{m}_{2}}=x\Rightarrow \frac{x+16}{32[x+1]}=\frac{8}{76} \Rightarrow 76x+76\times 16=8\times 32x+8\times 32 \Rightarrow 76x+1216=256x+256$

$960=180x\Rightarrow x=\frac{96}{18}=\frac{16}{3}$

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Solution

$\Rightarrow \frac{2}{25}=[\frac{{m}_{1}}{{m}_{2}}\times \frac{1}{32}+\frac{1}{2}]{m}_{2}...(1)$

$\Rightarrow {m}_{1}+{m}_{2}=0.76$

$\Rightarrow {m}_{2}[1+\frac{{m}_{1}}{{m}_{2}}]=\frac{76}{100}...(2)$

$(1)$ divided by $(2)$ ; $\frac{[\frac{{m}_{1}}{{m}_{2}}\times \frac{1}{32}+\frac{1}{2}]}{[\frac{{m}_{1}}{{m}_{2}}+1]}=\frac{2}{25}\times \frac{100}{76}$

Let assume,

$\Rightarrow \frac{{m}_{1}}{{m}_{2}}=x\Rightarrow \frac{x+16}{32[x+1]}=\frac{8}{76} \Rightarrow 76x+76\times 16=8\times 32x+8\times 32 \Rightarrow 76x+1216=256x+256$

$960=180x\Rightarrow x=\frac{96}{18}=\frac{16}{3}$

JEE Main 2021 — Physics Thermodynamics

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JEE Main 2021 — Physics Thermodynamics

Options

Did you get this right?

Solution

Your note

JEE Main Thermodynamics in other years

More JEE Main Thermodynamics questions

Other Physics topics for JEE Main

Mechanics

Electromagnetism

Modern Physics

Optics

Waves & Oscillations

Keep practicing Thermodynamics