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  • The molar heat capacity for an ideal gas at constant pressure is <img alt="20.785 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}" src="/latex-image/?20.785%20%5Cmathrm%7B%7EJ%7D%20%5Cmathrm%7B%7EK

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

Option: 1

2


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

We Know,
\mathrm{\Delta H= C{p}\Delta T\; and\: \Delta H= \Delta V-R\Delta T}  

\mathrm{So,Cp\Delta T= \Delta V-R\Delta T}
\mathrm{for\, n\, mole,nCp\Delta T= \Delta V-nR\Delta T}

\mathrm{\Delta V\; for\; gas= 5000\, J,}
\mathrm{\Delta T= 50.0\, K-300\, K= 200\, K}
\mathrm{Cp= 20.785\, J\, K^{-1}\, mol^{-1}}
\mathrm{R= 8.314\, J\, K^{-1}\, mol^{-1}}

Now,
\mathrm{n\times 200\times 20.785= 5000-n\times 8.314\times200 }
\mathrm{n= \frac{5000}{200\times 12.471}}
\mathrm{n= 2\, mol}

Ans =2

Posted by

Devendra Khairwa

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