Question

An insulated vertical cylinder Contains 0.1 kg Argon gas with the help of a frictionless non- conducting piston as shown in the figure . The mass of the piston is 5kg and initially rest on the bottom of the cylinder. The cylinder connected to nitrogen tank at 100 bar to a pipeline fitted with the valve The valve is opened and nitrogen slowly enters the cylinder. During this process the piston is lifted and to height of 10cm by Nitrogen gas. The initial pressure and temperature of argon are 300K and 1 bar. The final temperature of argon gas is 320K for argon R = 0.208 kJ/kgK and r = 1.67 Find the net work done by the Nitrogen

Answer 1

The net work done by the Nitrogen in lifting the mass and the pressure is; W_n = 0.6257 kJ

What is the net work done?

We are given;

Mass of argon; m_a = 0.1 kg

mass of piston; m_p = 5 kg

Pressure 1; p₁ = 100 kPa

Temperature 1; T₁ = 300 K

Temperature 2; T₂ = 320 K

Ideal gas constant; R = 0.208 kJ/kg.K

γ = 1.67

Since the reaction is adiabatic and slowly reversible, then we will use the formula; PV^(γ) = C

Thus, work done by argon is;

W_ar = [m_a * R(T₁ - T₂)]/(γ - 1)

W_ar = [0.1 * 0.208(300 - 320)]/(1.67 - 1)

W_ar = -0.6028 kJ

Work done by nitrogen will be;

W_n = |W_ar| + (m_p * g * m_a)/1000

W_n = 0.6028 + (5 * 9.81 * 0.1)/1000

W_n = 0.6257 kJ

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