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At \mathrm{298 \mathrm{~K}}, an ideal monoatomic gas was expanded so that the volume becomes \mathrm{4 \mathrm{~L}} from \mathrm{1 \mathrm{~L}}. Also, \mathrm{5} moles of the same gas when underwent a reversible process it was found that \mathrm{P V^2=C}. Find \mathrm{\Delta H} for the same.

Option: 1

\mathrm{2793.75\ R}


Option: 2

\mathrm{2801\ R}


Option: 3

\mathrm{2.7937\ R}


Option: 4

\mathrm{2.801\ R}


Answers (1)

best_answer

\begin{aligned} &\mathrm{ P_2 V_2^2=P_1 V_1^2} \\ &\mathrm{ \frac{P_2}{P_1}=\left(\frac{V_1}{V_2}\right)^2} \end{aligned}
\mathrm{\text { Now, }} \begin{aligned}\\\\ \mathrm{\frac{T_2}{T_1}} &\mathrm{ =\frac{P_2 V_2}{P_1 V_1}=\frac{V_1}{V_2}=\frac{1}{4}} \\ \mathrm{T_2} & =\frac{298}{4}=74.5 \mathrm{~K} \end{aligned}
\mathrm{\begin{aligned} \Delta \mathrm{H} & =\mathrm{n C_p \Delta T} \\ & =5 \times \frac{5}{2}\ \mathrm{R}\ (-223.5) \\ & =2793.75\ \mathrm{R} \end{aligned}}

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Rakesh

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