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 open, 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, in kJ/kg, and the finial temperature of the helium in the tank. Neglect all kinetic and potential energy effects.

Answer 1

Answer: a 8143.71 kJ/kg

b 393.15 K

Explanation:

This system is an isobaric process in which there is no change in pressure a quasistatic process where a pressure distribution exists

a since no change in pressure =0 the system does work thus

FOR HELIUM  properties in standard thermodynamic chart

cv = 3.1 kJ/kgK

M = Molar mass = 4 kg/kmol

R = Universal gas constant = 8.314 kJ/kg K

cp ≈ cv +R /M = 3.1 + 8.314 /4 = 5.1785 kJ/kgK  

Cp = cp * M = 5.1785 kJ/kgK * 4 kg/kmol  = 20.714 kJ/kgkmol

T = 120  °C  to Kelvin = 120 + 273.15k = 393.15 K

W =n Cp ΔT = 1 kmol * 20.714 kJ/kg kmol* 393.15 K = 8143.71 kJ/kg

b convert T °C = T K thus 120 + 273.15 K = 393.15 K

P₁/T₁ = P₂/T₂

200 kPa/ 393.15 K = 200 kPa/T₂

T₂ = 200 kPa * 393.15 K/ 200 kPa = 393.15 K or 120 k