Answer to Question #100474 in Astronomy | Astrophysics for Garvin

Question

. Hydrogen has a density of 89.9 grams per cubic meter at a certain temperature and a certain pressure. Calculate the volume in cubic meters of hydrogen having a mass of 0.1 kilogram at the same temperature and pressure.

Answer 1

We write the Mendelev-Clapeyron equation for the first case

$PV_1=\frac{m_1}{\mu}RT$

we write the equation in another form

$P=\frac{m_1}{\mu V_1}RT$

Where

$\frac{m_1}{V_1}=\rho_1=89.9{g/m^3}=0.0899{kg/m^3}$

then we get the equation

$P=\frac{\rho_1}{\mu}RT$ (1)

We write the Mendelev-Clapeyron equation for the second case

$PV_2=\frac{m_2}{\mu}RT$ (2)

divide equation (2) by equation (1)

$\frac{PV_2}{P}=\frac{\frac{m_2}{\mu}RT}{\frac{\rho_1}{\mu}RT}$

we reduce such terms, we get

$\frac{V_2}{1}=\frac{m_2}{\rho_1}$

or $V_2=\frac{m_2}{\rho_1}=\frac{0,1}{0,0899}=1.112m^3$