Question

A rigid, insulated tank that is initially evacuated is connected through a valve to a supply line that carries helium at 200 kPa and 120°C. Now the valve is opened, and helium is allowed to flow into the tank until the pressure reaches 200 kPa, at which point the valve is closed. Determine the flow work of the helium in the supply line and the final temperature of the helium in the tank.

Answer 1

Answer:

T=655K, W=816kJ/kg

Explanation:

consulting the properties of gases, for Helium we have,

$R=2.0769kJ/kg.K,\\c_p=5.1926kJ/kg.K,\\c_v=3.1156kJ/kg.K,$

To find the specific volume we use the equation,

$v=\frac{RT}{P}$

Substituting,

$v=\frac{2.0769*(120+273)}{200*10^3}\\v=4.08m^3/kg$

Flow work is gived by,

$W_{flow}=Pv\\W_{flow}=200*10^3*4.08=816kJ/kg$

To find the temperature of the gas in the tank we need

$u_{tank}=h_{line}\\h_{line}=c_pT_{line}\\u_{tank}=c_vT_{tank}$

So,

$T_{tank}=\frac{c_p T_{line}}{c_v}\\T_{tank}=\frac{5.1926}{3.1156}*343\\T_{tank}=655K$