1. Tardigrade
  2. Question
  3. Chemistry
  4. The molar heat capacity for an ideal gas at constant pressure is 20.785 J K -1 mol -1. The change in internal energy is 5000 J upon heating it from 300 K to 500 K. The number of moles of the gas at constant volume is [Nearest integer] (Given: R =8.314 J K -1 mol -1 )

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Q. The molar heat capacity for an ideal gas at constant pressure is $20.785 \,J\, K ^{-1} mol ^{-1}$. The change in internal energy is $5000\, J$ upon heating it from $300 \,K$ to $500\, K$. The number of moles of the gas at constant volume is _____ [Nearest integer]
(Given: $R =8.314 \,J \,K ^{-1} mol ^{-1}$ )

JEE MainJEE Main 2022Thermodynamics

Solution:

$C _{ p , m }= C _{ v , m }+ R$
$ \Rightarrow C _{ v , m }=20.785-8.314=12.471 J k ^{-1} ml ^{-1} $
$ \Delta U = nC _{ v , m } \Delta T$
$ \Rightarrow n =\frac{5000}{12.471 \times 200}=\frac{25}{12.471} \approx 2$