1.7(a) In an attempt to determine an accurate value of the gas constant, $R$, a student heated a container of volume $20.000 \mathrm{dm}^3$ filled with $0.25132 \mathrm{g}$ of helium gas to $500^{\circ} \mathrm{C}$ and measured the pressure as $206.402 \mathrm{cm}$ of water in a manometer at $25^{\circ} \mathrm{C}$. Calculate the value of $R$ from these data. (The density of water at $25^{\circ} \mathrm{C}$ is $0.99707 \mathrm{g} \mathrm{cm}^{-3}$; a manometer consists of a U-shaped tube containing a liquid. One side is connected to the apparatus and the other is open to the atmosphere. The pressure inside the apparatus is then determined from the difference in heights of the liquid.)
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