Thermodynamics Tutorial No.2 Energy Transfer

1. A gas undergoes compression from an initial state of V₁ =0.1 m³, P₁ =200 KPa to a final state of V₂ =0.04 m³, P₂ =500 KPa. If the pressure varies linearly with volume during the process, determine the work transfer.

2. A gas undergoes  a polytropic process from an initial of 500 KPa and 0.02 m³ to a final state of 100 KPa and 0.05 m³. Determine the work transfer.
3. In a non flow process,a gas expands from volume 0.1 m³ to a volume of 0.2 m³, according to the law : P =2/V +1.5 where P is the pressure in bar, and V is the volume is m³. Determine (i) the process at the end of the expansion and (ii) the work done by the gas in the expansion process in kJ.

4. Consider a two part process with an expression from 0.1 m³ to 0.2 m³ at a constant pressure of 150 KPa followed by an expression from 0.2 m³ to 0.4 m³ with a linearly rising pressure from 150 KPa ending at 300 KPa. Show the process in a P-V diagram and find the boundary work.

5. Air undergoes three process in series to form a cycle: Process 1-2: constant volume cooling, V₁ = V₂ =2 m³ Process 2-3: constant pressure heating, P =100 KPa, V₁ = 10 m m³ Process 3-1: isothermal compression

6. Argon (1 kg) contained in a piston cylinder device shown in Figure P2.6 is initially at a pressure of 500 KPa and a temperature of 70°C. Heat is added until the final temperature is 600°C and a pressure
of 1 MPa is required to lift the piston form the stops. Sketch the process on P-V and T-V diagrams and determine the total work transfer. [Take R =208 J/kg k]

7. Air (0.5 kg) in the piston cylinder shown in Figure P2.7 has an initial pressure and temperature of 1 MPa and 500°C repectively. The system is
cooled until the temperature reaches 50°C. It takes a pressure of 0.5 MPa to support the piston. Sketch the process on P-V and T-V diagrams and determine the total the total work transfer. [Take R = 287 J/kg k]

8. Oxygen (3.6 kg) contained in a piston cylinder device shown in Figure P2.8 is initially at a pressure of 200 KPa and temperature of 50°C. Heat is ³. It requires a pressure of 500 KPa to lift the piston. Sketch the process on P-V and T-V diagrams and determine the total work transfer. [Take R =260 J/kg k]
added until the piston just reaches the upper stops where the total volume is 3 m

9. A piston cylinder device shown in Figure P2.9 contains 1 kg of Nitrogen initially at a pressure of 250 KPa and a temperature of 500°C.Heat is lost from the system till its temperature reaches 25°C. Sketch the process on P-V and T-V diagrams and determine the final pressure and the total work transfer. [Take R =297 J/kg k]

10. A piston cylinder arrangement loaded with a linear spring (k =2 kN/m) as shown in Figure P2.10 contains air. Spring is initially unstretched and undergoes a compression of 40 mm during a process. If the mass of the piston is 80 kg and piston diameter is 0.1 m, determine the total work transfer. [Take P_atm = 100 KPa and g =9.8 m/s²]

11. Air (0.01 kg) is contained in a piston cylinder device restrained by a linear spring (k = 500 kN/m) as skown in Figure P2.11. Spring initially touches the piston but exerts no force on it. Heat is added to the system until the piston is displayed upward by 80 mm. Determine (a) the temperature at which piston leaves the stops (b) work done by air [Take R = 287 j/kg k, P^atm = 100 KPa and g = 9.81 m/s²]

12. A piston cylinder arrangement shown in Figure P2.12 is restrained by two linear springs as shown. The system contains air initially at a pressure of 150 KPa and a volume of 0.002 m³. Heat is added to the system until its volume doubles; determine the total work transfer. Also sketch the process on P-V diagram. Both springs have spring constant of 100 kN/m.