MES 2025 Unit 1 Assignment 1 - Numerical

A gas undergoes an isothermal expansion from P1=2 MPa to P2=0.5 MPa. The initial volume is V1=0.1 m3. Calculate the work done by the system.

• 138.6 kJ

• 277.3 kJ

• 415.9 kJ

• 554.5 kJ

A gas undergoes polytropic expansion (n=1.25) from P1=500 kPa, V1=0.2 m3 to V2=0.8 m3. Calculate the work done.

• 240 kJ

• 320 kJ

• 400 kJ

• 480 kJ

A system undergoes a cyclic process with the following data: Q₁ = +150 kJ, Q₂ = -80 kJ, W₁ = +100 kJ, W₂ = -30 kJ. The third heat transfer Q₃ is:

• 0 kJ

• -40 kJ

• +40 kJ

• -70 kJ

A closed system receives 200 kJ of heat while performing 120 kJ of work. The change in internal energy is:

• 80 kJ

• 320 kJ

• -80 kJ

• -320 kJ

A hydraulic turbine receives water at 2000 kW mechanical power and generates 1600 kW electrical power with generator efficiency of 90%. The turbine mechanical efficiency is:

• 80%

• 85%

• 88.9%

• 92%

Water is pumped at 50 L/s to a height of 25 m. Assuming 100% efficiency and neglecting losses, the minimum power required is: (Take g = 9.81 m/s², ρ = 1000 kg/m³)

• 10.2 kW

• 12.3 kW

• 14.5 kW

• 16.8 kW

A motor rotates at 1500 rpm with a torque of 200 N·m. The shaft power developed is:

• 26.2 kW

• 31.4 kW

• 36.8 kW

• 42.1 kW

For an adiabatic process with γ = 1.4, if P₁ = 1000 kPa, V₁ = 0.5 m³, P₂ = 200 kPa, the work done is:

• 625 kJ

• 750 kJ

• 875 kJ

• 1000 kJ

2 kg of liquid with specific heat 3 kJ/kg·K is stirred in an insulated chamber. If temperature rises by 20°C, the work done on the system is:

• -120 kJ

• +120 kJ

• -60 kJ

• +60 kJ

A pump-motor unit consumes 25 kW electrical power to pump water 30 m high at 60 L/s. The overall efficiency is: (Take g = 9.81 m/s², ρ = 1000 kg/m³)

• 65.4%

• 70.6%

• 75.8%

• 80.2%