Answer
Calculate the density of Helium by using the following equation:
$$
\rho=\frac{p}{R T} \ldots \ldots(1)
$$
Here, density of ideal gas is $\rho$, Absolute pressure is $p$, and gas constant is $R$ absolute
temperature is $T$
Sample calculation:
Gas constant for Helium is $2077 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}$
Substitute $50 \times 10^{3} \mathrm{~N} / \mathrm{m}^{2}$ for $p, 2077 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}$ for $R$, and $50{ }^{\circ} \mathrm{C}$ for $T$ in the equation $(1)$
$$
\begin{aligned}
\rho &=\frac{50 \times 10^{3}}{2077 \times(50+273)} \\
&=\frac{50 \times 10^{3}}{670871} \\
&=0.0745 \mathrm{~kg} / \mathrm{m}^{3}
\end{aligned}
$$
Calculate remaining density values by varying pressure and temperature values and tabulate the values:
$$
\begin{array}{|l|l|l|l|}
\hline \begin{array}{l}
\text { Pressure in } \\
\mathrm{kPa}
\end{array} & \begin{array}{l}
\text { Temperature in degree } \\
\text { Celsius }
\end{array} & \begin{array}{l}
\text { Gas constant for Helium in } \\
\mathrm{J} / \mathrm{kg}-\mathrm{K}
\end{array} & \begin{array}{l}
\text { Density in } \\
\mathrm{kg} / \mathrm{m}^{3}
\end{array} \\
\hline 50 & 50 & 2077 & 0.0745 \\
\hline 100 & 100 & 2077 & 0.129 \\
\hline 200 & 200 & 2077 & 0.1707 \\
\hline
\end{array}
$$
Work Step by Step
Calculate the density of Helium by using the following equation:
$$
\rho=\frac{p}{R T} \ldots \ldots(1)
$$
Here, density of ideal gas is $\rho$, Absolute pressure is $p$, and gas constant is $R$ absolute
temperature is $T$
Sample calculation:
Gas constant for Helium is $2077 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}$
Substitute $50 \times 10^{3} \mathrm{~N} / \mathrm{m}^{2}$ for $p, 2077 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}$ for $R$, and $50{ }^{\circ} \mathrm{C}$ for $T$ in the equation $(1)$
$$
\begin{aligned}
\rho &=\frac{50 \times 10^{3}}{2077 \times(50+273)} \\
&=\frac{50 \times 10^{3}}{670871} \\
&=0.0745 \mathrm{~kg} / \mathrm{m}^{3}
\end{aligned}
$$
Calculate remaining density values by varying pressure and temperature values and tabulate the values:
$$
\begin{array}{|l|l|l|l|}
\hline \begin{array}{l}
\text { Pressure in } \\
\mathrm{kPa}
\end{array} & \begin{array}{l}
\text { Temperature in degree } \\
\text { Celsius }
\end{array} & \begin{array}{l}
\text { Gas constant for Helium in } \\
\mathrm{J} / \mathrm{kg}-\mathrm{K}
\end{array} & \begin{array}{l}
\text { Density in } \\
\mathrm{kg} / \mathrm{m}^{3}
\end{array} \\
\hline 50 & 50 & 2077 & 0.0745 \\
\hline 100 & 100 & 2077 & 0.129 \\
\hline 200 & 200 & 2077 & 0.1707 \\
\hline
\end{array}
$$
