JEE Main 2021 — Chemistry Physical Chemistry

2021integerhard

Five moles of an ideal gas at $293K$ is expanded isothermally from an initial pressure of $2.1\mathrm{MPa}$ to $1.3\mathrm{MPa}$ against at constant external pressure $4.3\mathrm{MPa}$ . The heat transferred in this process is ___ ${\mathrm{kJmol}}^{-1}$ . (Rounded-off to the nearest integer)[ Use $R=8.314J{\mathrm{mol}}^{-1}{K}^{-1}$ ]

Official previous-year question

Held on 25 Feb 2021 · Verified 6 Jul 2026.

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Solution

$n=5,T=293K=\mathrm{const},\Delta U=0$

${P}_{1}=2.1\mathrm{MPa},{P}_{2}=1.3\mathrm{MPa}$

${P}_{\mathrm{ext}}=4.3\mathrm{MPa}=\mathrm{const}.$

$W=-{P}_{\mathrm{ext}}({V}_{2}-{V}_{1})=-{P}_{\mathrm{ext}}(\frac{\mathrm{nRT}}{{P}_{2}}-\frac{\mathrm{nRT}}{{P}_{1}})$

or, $W=-{P}_{\mathrm{ext}}\mathrm{nRT}(\frac{1}{{P}_{2}}-\frac{1}{{P}_{1}})$

$=-4.3\times 5\times 8.314\times 293(\frac{1}{1.3}-\frac{1}{2.1})$

$=-4.3\times 5\times 8.314\times 293(\frac{2.1-1.3}{1.3\times 2.1})$

$=-15347.7J$

or, $W=-15.35\mathrm{kJ}$

$\Delta {U}^{0}=q+W$

$\therefore q=-W$

or, $q=15.35\mathrm{kJ}$ (for $5$ moles)

$\therefore q/\mathrm{mole}=\frac{15.35}{5}=3\mathrm{kJ}{\mathrm{mol}}^{-1}$

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JEE Main 2021 — Chemistry Physical Chemistry

2021integerhard

Official previous-year question

Held on 25 Feb 2021 · Verified 6 Jul 2026.

Did you get this right?

Solution

$n=5,T=293K=\mathrm{const},\Delta U=0$

${P}_{1}=2.1\mathrm{MPa},{P}_{2}=1.3\mathrm{MPa}$

${P}_{\mathrm{ext}}=4.3\mathrm{MPa}=\mathrm{const}.$

$W=-{P}_{\mathrm{ext}}({V}_{2}-{V}_{1})=-{P}_{\mathrm{ext}}(\frac{\mathrm{nRT}}{{P}_{2}}-\frac{\mathrm{nRT}}{{P}_{1}})$

or, $W=-{P}_{\mathrm{ext}}\mathrm{nRT}(\frac{1}{{P}_{2}}-\frac{1}{{P}_{1}})$

$=-4.3\times 5\times 8.314\times 293(\frac{1}{1.3}-\frac{1}{2.1})$

$=-4.3\times 5\times 8.314\times 293(\frac{2.1-1.3}{1.3\times 2.1})$

$=-15347.7J$

or, $W=-15.35\mathrm{kJ}$

$\Delta {U}^{0}=q+W$

$\therefore q=-W$

or, $q=15.35\mathrm{kJ}$ (for $5$ moles)

$\therefore q/\mathrm{mole}=\frac{15.35}{5}=3\mathrm{kJ}{\mathrm{mol}}^{-1}$

Your note

JEE Main Physical Chemistry in other years

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JEE Main 2021 — Chemistry Physical Chemistry

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JEE Main Physical Chemistry in other years

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JEE Main 2021 — Chemistry Physical Chemistry

Did you get this right?

Solution

Your note

JEE Main Physical Chemistry in other years

More JEE Main Physical Chemistry questions

Other Chemistry topics for JEE Main

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Inorganic Chemistry

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