JEE Main 2022 — Chemistry Physical Chemistry

2022integermedium

The molar heat capacity for an ideal gas at constant pressure is $20.785J{K}^{-1}{\mathrm{mol}}^{-1}$ . The change in internal energy is $5000J$ upon heating it from $300K$ to $500K$ . The number of moles of the gas at constant volume is____

(Given: $R=8.314J{K}^{-1}{\mathrm{mol}}^{-1}$ )

Official previous-year question

Held on 27 Jul 2022 · Verified 6 Jul 2026.

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Solution

Molar specific heat capacity at constant pressure is defined as the amount of heat energy required to raise the temperature of one mole of a substance through $1K$ or $1^{\circ}C$ at constant pressure. It is denoted by ${C}_{p,m}$ .

Molar specific heat capacity at constant volume is defined as the amount of heat energy required to raise the temperature of one mole of a substance through $1K$ or $1^{\circ}C$ at constant volume. It is denoted by ${C}_{v,m}$ .

${C}_{v,m}=\frac{1}{n}\frac{\Delta U}{\Delta T}$

${C}_{p,m}={C}_{v,m}+R$

$\Rightarrow {C}_{v,m}=20.785-8.314=12.471{\mathrm{Jk}}^{-1}{\mathrm{ml}}^{-1}$

$\Delta U={\mathrm{nC}}_{v,m}\Delta T$

$\Rightarrow n=\frac{5000}{12.471\times 200}=\frac{25}{12.471}\approx 2$

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JEE Main 2022 — Chemistry Physical Chemistry

2022integermedium

(Given: $R=8.314J{K}^{-1}{\mathrm{mol}}^{-1}$ )

Official previous-year question

Held on 27 Jul 2022 · Verified 6 Jul 2026.

Did you get this right?

Solution

${C}_{v,m}=\frac{1}{n}\frac{\Delta U}{\Delta T}$

${C}_{p,m}={C}_{v,m}+R$

$\Rightarrow {C}_{v,m}=20.785-8.314=12.471{\mathrm{Jk}}^{-1}{\mathrm{ml}}^{-1}$

$\Delta U={\mathrm{nC}}_{v,m}\Delta T$

$\Rightarrow n=\frac{5000}{12.471\times 200}=\frac{25}{12.471}\approx 2$

Your note

JEE Main Physical Chemistry in other years

Keep practicing Physical Chemistry

Work through every JEE Main Physical Chemistry PYQ, year by year.

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JEE Main 2022 — Chemistry Physical Chemistry

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Solution

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JEE Main Physical Chemistry in other years

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JEE Main 2022 — 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

Organic Chemistry

Inorganic Chemistry

Keep practicing Physical Chemistry