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  4. 2.2 g of nitrous oxide ( N 2 O ) gas is cooled at a constant pressure of 1 atm from 310 K to 270 K causing the compression of the gas from 217.1 mL to 167.75 mL. The change in internal energy of the process, Δ U is ' -x prime J. The value of ' x ' is [nearest integer] (Given: atomic mass of N =14 g mol -1 and of O=16 g mol -1 Molar heat capacity of N 2 O is 100 JK -1 mol -1 )

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Q. $2.2\, g$ of nitrous oxide $\left( N _{2} O \right)$ gas is cooled at a constant pressure of $1 atm$ from $310\, K$ to $270\, K$ causing the compression of the gas from $217.1 \,mL$ to $167.75 \,mL$. The change in internal energy of the process, $\Delta U$ is ' $-x^{\prime} J$. The value of ' $x$ ' is __ [nearest integer]
(Given: atomic mass of $N =14\, g \,mol ^{-1}$ and of $O=16 \,g \,mol ^{-1}$
Molar heat capacity of $N _{2} O$ is $100\, JK ^{-1} \,mol ^{-1}$ )

JEE MainJEE Main 2022Thermodynamics

Solution:

$N _{2} O$ moles $=\frac{2.2}{44}=\frac{1}{20}$
$\Delta H = nC _{ p } \Delta T =\frac{1}{20} \times 100(-40)=-200 \,J$
$\Delta U = q _{ p }+ w$
$W =- P _{ ext } \Delta V$
$W =-1 \frac{(167.75-217.1)}{1000} \times 101.3\, J$
$W =+5 J$
$\Delta U =-200+5=-195 \,J$