Molar heat capacity ideal constant |ThermodynamicJEEMain2022

JEE MAIN 2022

27-07-2022 S1

Question

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 J upon heating it from 300 K to 500 K . The number of moles of the gas at constant volume is $\_\_\_\_$ [Nearest integer] (Given: $\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ )

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Solution

$\begin{aligned} \mathrm{C}_{\mathrm{Rm}}= & \mathrm{C}_{\mathrm{Km} m}+\mathrm{R} \\ \Rightarrow \quad & \mathrm{C}_{\mathrm{vm}}=20.785-8.314=12.471 \mathrm{~J} \mathrm{kf}^{-1} \mathrm{ml}^{-1} \\ & \Delta \mathrm{U}=\mathrm{nC}_{\mathrm{Km}} \Delta \mathrm{T} \\ \Rightarrow \quad & \mathrm{n}=\frac{5000}{12.471 \times 200}=\frac{25}{12.471} \approx 2\end{aligned}$

Question Tags

JEE Main

Chemistry

Easy

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