The density of $H e$ is $0.1784 k g / m^{3}$ at STP. If a given mass of $H e$ at STP is allowed to expand to $1.5$ times its initial volume by changing the temperature and pressure, compute its resultant density.

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Solution

$d_{H e} = 1.784 k g / m^{3}$ at STP

$A / q,; V_{f} = 1.5 \times V_{i}$

By mass conservation:

$: m_{f} = m_{i} = c o n s t a n t$

$∴ d_{i} = \frac{m_{i}}{V_{i}}$

$\Rightarrow d_{f} = \frac{m_{f}}{V_{f}} = \frac{m_{i}}{1.5 V_{i}} = \frac{d_{i} \times V_{i}}{1.5 \times V_{i}} = \frac{0.1784}{1.5} = 0.1189 K g / m^{3}$

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