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: $\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$)
Answer (integer)
2
Solution
$\mathrm{C}_{\mathrm{p}}=20.785 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$
<br/><br/>
$$
\begin{aligned}
&\text { and } \Delta \mathrm{U}=\mathrm{nC} \mathrm{v} \Delta \mathrm{T} \\\\
&\therefore \quad \mathrm{nC}_{\mathrm{v}}=\frac{5000}{200}=25
\end{aligned}
$$
<br/><br/>
and we know that
<br/><br/>
$$
\begin{aligned}
&C_{p}-C_{v}=R \\\\
&20.785-\frac{25}{n}=8.314 \\\\
&n=\frac{25}{(20.785-8.314)}=2
\end{aligned}
$$
About this question
Subject: Chemistry · Chapter: Thermodynamics · Topic: Zeroth and First Law
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