Question

A sample of $2kg$ monoatomic helium gas (assumed ideal) is taken through the process $ABC$ and another sample of $2kg$ of the same gas is taken through the process $ADC$ . Given that the molecular mass of helium = $4amu$ , find the temperature of helium in the state $D$ . $[$ Take the universal gas constant $R=\frac{25}{3}Jmo{l}^{-1}{K}^{-1}]$

Answer 1

Answer: 240

Number of gram moles of He, $n=\frac{m}{M}=\frac{2\times 10^3}{4}=500$ mole
$\begin{array}{l}{V}_A=10m^3,P_A=5\times 10^{4}N/m^2\\ T_A=\frac{P_A{V}_A}{nR}=\frac{(10)\left(5\times 10^4\right)}{(500)\left(\frac{25}{3}\right)}K=120K\end{array}$
Similarly, $V_B=10m^3,P_B=10\times 10^{4}N/m^2$
$T_B=\frac{(10)\left(10\times 10^4\right)}{(500)\left(\frac{25}{3}\right)}K=240K$
Similarly, $V_C=20m^3,P_C=10\times 10^{4}N/m^2$
$T_C=\frac{(20)\left(10\times 10^4\right)}{(500)\left(\frac{25}{3}\right)}K=480K$
Similarly, $V_D=20m^3,P_D=5\times 10^{4}N/m^2$
$T_D=\frac{(20)\left(5\times 10^4\right)}{(500)\left(\frac{25}{3}\right)}K=240K$